Book Reviews

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Dependence Modeling With Copulas.

Harry Joe. New York: Chapman & Hall/CRC Press, 2014, xviii + 462 pp., $89.95 (H), ISBN: 978-1-46-658322-1.

In a recent interview, Paul Embrechts named Harry Joe’s (1997) book as one of the three most important contributions to the field “Dependence Modeling;” its more than 4000 citations (by mid 2015) numerically emphasize this assessment. So what should the reader expect from Joe’s latest volume?

First, it is important to stress that this is not simply a revised version. It truly is a new book. Comparing both works reflects how fast the field has accrued in less than two decades. Many of the ideas that had been briefly sketched in the 1997 book have now grown into independent sub-fields of research, a prominent example being vine copulas. Copula theory was developed in a fruitful collaboration by contributors from Analysis, Probability, Statistics, and recently Computer Sciences. The point of view in the current book is that of model building and applications in Statistics, emphasizing the role of models for the density, rather than for distribution functions or stochastic representations. Second, the style of this book is noticeably different. Each chapter starts with a useful survey and is divided in many subsections. Proofs are postponed to the last chapter or cited, which makes the text compact and easier to follow. Some readers, however, might have preferred the traditional “proof after statement” structure. Many paragraphs contain long collections of facts and references without detailed explanations. This truly has encyclopedic value for experts, but might be too much information for a novice. Third, the book is an interesting combination of Harry Joe’s personal vision and the “zeitgeist,” especially with respect to the fast-growing vine-copula community. Let us now dive into the individual chapters.

The first chapter introduces elementary multivariate (non-Gaussian) distributions and illustrates the basic steps of copula modeling (two-step inference) by means of real data examples. It also contains interesting remarks on the origins of many concepts.

Chapter 2 is a comprehensive collection of important computation rules for copulas, multivariate dependence concepts and measures beyond correlation, and a discussion of possible stylized facts a copula model can admit (tail dependence, asymmetry, etc.). Many arguments and examples are provided to emphasize that nonnormal models are needed for real-world applications. The necessary tools to construct and analyze such models are introduced.

The next chapter is devoted to general construction principles for copulas. This ranges from exchangeable models over single- and multi-factor models to pair-copula constructions. Well-known families of distributions are mentioned for illustration and are put into the perspective of these more general categories. Classical and hierarchical Archimedean copulas are discussed in detail, including their stochastic origin. Both discrete data and mixed data examples are discussed, topics that most books omit. Summarizing, Chapter 3 provides an excellent survey of the state of the art in—and historical background of—copula model design.

Chapter 4 could have been published as a stand-alone “encyclopedia of copula families.” It lists an impressive number of parametric families, including their properties, origin, and possible multivariate generalizations. Survey tables provide structure and facilitate cross-comparisons. I anticipate this chapter will be especially valuable for researchers that are working with some copula family and need a reference guide for its properties and a link to the deeper literature. The opposite direction, that is, being guided to select a copula family to match a real data situation, would have been easier with scatter- and density plots for each family. Although these are omitted to save space, they can be produced using the companion software.

The fifth chapter contains parametric and nonparametric estimation strategies and diagnostic tools. The two-step inference philosophy (first estimating the marginal laws, followed by an estimation of the copula) that is at the heart of copula modeling is explained in detail. A very interesting section is devoted to the identification of wrongly specified models by means of the Kullback–Leibler divergence.

The sixth chapter explicitly acknowledges the prominent role of computational statistics with multivariate data. It contains 30 algorithms, written in generic pseudo-code, for various problems in simulation, estimation, and model selection; with a strong tilt toward algorithms around vine copulas. Most of the algorithms are explained or illustrated. This chapter is clearly valuable for someone who is implementing the presented concepts, and is interesting addition to the theoretical concepts. Unfortunately, not all algorithms are discussed with respect to efficiency and mentioning the names of available R-packages with the algorithms would have been useful; though an important source of further information is given on the authors website http://copula.stat.ubc.ca/.

Chapter 7 contains case studies based on real and simulated data, with applications ranging from finance and insurance to the modeling of environmental phenomena. This chapter allows one to follow the genuine process of model design step-by-step. For some datasets links are given so that one can replicate the modeling exercise. Again, the author’s website is a rich source for almost all examples mentioned in the book. This chapter illustrates the many difficulties one faces in real-world situations and explains the decisions that must be taken to arrive at a parsimonious and realistic model.

The last chapter, called “Theorems for Properties of Copulas,” contains many proofs of statements made in preceding chapters. These proofs are well written and references to the original sources are provided. Unfortunately, there are no explicit references back to earlier chapters where the corresponding statements are used.

In sum, I consider this book a “must have” for someone seriously involved in dependence modeling with copulas, especially with a focus on modeling real data. The huge collection of facts and references for certain families of copulas, dependence measures, and statistical tools makes this book a valuable reference for researchers and experienced practitioners. I expect the statistical approach to the field “Dependence Modeling” will be especially appealing for the JASA audience. Novices in the field may, however, be overwhelmed by the pure amount of information and may prefer a subset of information with more explanations. Concerning possible improvements, the layout of the presented figures might be beautified and made consistent. Moreover, the typesetting has occasional inconsistencies like the use of “Kendall’s tau” versus “Kendall’s $τ$.”

Matthias Scherer

Technische Universität München

Hierarchical Modeling and Analysis for Spatial Data (2nd ed.).

Sudipto Banerjee, Bradley P.Carlin, and Alan E. Gelfand. New York: Chapman & Hall/CRC Press, 2014, xxi + 562 pp., $99.95 (H), ISBN: 978-1-43-981917-3.

If you want a thorough taste of the spatial statistics field, Hierarchical Modeling and Analysis for Spatial Data is definitely a book for you. It is accessible and comprehensive, and it fully explores how useful spatial statistics can be without sacrificing the theory it is grounded in. This is a great book for graduate students and professors who want to understand the theoretical underpinnings of the field as well as practitioners who want a toolkit for tackling spatial problems. Most chapters introduce a topic with a very pragmatic question, for example, “If we are handed a spatiotemporal dataset, how should we analyze it?” The authors then develop the theory necessary to answer the pragmatist’s question, and then they provide several real-world data analyses to illustrate. Many chapters also include a section explaining how to perform exploratory data analysis (EDA), which many practitioners will find useful. These examples include graphs and tables (as they should), but also R and WinBUGS code that shows how the analysis was done. And if the reader does not want to retype code printed in a book, they are in luck; the authors provide an easy-to-use online resource with all of the book’s code and datasets. Indeed, these examples are so comprehensive that readers could learn a lot by simply going through them. The accessible theoretical material paired with these detailed examples make Hierarchical Modeling and Analysis for Spatial Data an especially substantial and worthwhile investment.

The authors clearly have a modeling-first perspective, which results in a particularly readable text with a good balance between theory and applications. The authors walk the reader through theoretical material with practical questions such as, “What kind of data are we looking at? How should we model it?” For example, Chapter 4 introduces areal data with reasonable questions about this type of data: “Is there a spatial pattern? How can we model the interdependence between a particular area and other areas?” These questions lead to exploring theoretical material such as Markov random fields, which are necessary for implementing conditionally auto-regressive (CAR) models for areal data. This structure allows the authors to explore each major topic in the book with a model-building approach without watering down the theory. Nonetheless, the authors are friendly enough to mark more mathematically advanced sections with a star so that these sections can either be avoided or sought out (as per one’s tastes).

The deep connections the authors make between the theory and the examples show not only the authors’ expertise but also how far spatial statistics has come since the publication of the first edition ten years ago. The authors have clearly taken the time to think about how to best organize and present the material in this new edition. The first edition included exploratory tools for point-referenced data (now Chapter 2) as well as areal data (Chapter 4), a review of hierarchical Bayesian modeling (Chapters 5 and 6), multivariate modeling (Chapters 9 and 10), and spatiotemporal modeling (Chapter 11). There is a lot of new material in the second edition; indeed, the second edition is over 50% larger than the first.

In particular, Chapter 8 is an entirely new, 55-page chapter on point-pattern data. The authors present the topic with a Bayesian modeling lens—a perspective on the topic that is difficult to find elsewhere. The authors elaborate on many EDA tools for point-pattern data, including an alphabet’s-worth of functions (such as F, G, J, K, and L functions). The authors also explore many processes that can be used to model point-pattern data, including cluster, Neyman–Scott, shot noise, and Gibbs processes. In short, this is a must-read chapter for any practitioner who needs to model point-pattern data.

There are several other new chapters that practitioners and academics alike may find useful. Chapter 12 is a toolbox for analyzing big data: the toolbox includes variational Bayes methods, low rank models for dimension reduction, and predictive process models. Chapter 13 is about spatial gradients and wombling, and it would be difficult to find so much information on this topic in another place. Banerjee and Gelfand wrote several papers that arguably first developed the theory and modeling tools for spatial gradients and derivative processes, and so this chapter is a very comprehensive review of the topic. There is also a new (and starred) chapter expanding on the theory of point-referenced data for readers who want a more formal introduction to the topic (Chapter 3). Finally, there is new material on a few other special topics (data fusion/assimilation and spatially varying coefficient models) and almost twice as many exercises, which is nice for teachers who may already be using this book for a class.

This book could serve as a course textbook, although there are a few prerequisites. First, some general knowledge of stochastic processes is a must. Because the authors view spatial statistics through a Bayesian lens, some decent knowledge of Bayesian analysis and hierarchical modeling would also be helpful. The book is fairly accessible given these prerequisites, making for a target audience of advanced graduate students and researchers looking for a modeling approach to spatial data. Instructors teaching a graduate-level course in spatial statistics should absolutely consider this book for their students; the authors’ balance of theoretical material and real-world examples with R and WinBUGS code is already a very appropriate curriculum. Furthermore, the authors are clear where theory is lacking; for example, they acknowledge that Chapter 5, a review of Bayesian inference, is only a review. Luckily, each chapter includes citations to many foundational texts that readers and instructors can use for supplementary materials.

Indeed, the authors do not hold back on their references. Readers would be hard-pressed to find a page in the book that did not mention at least one or two papers. Some could view this book as a spatial statistics biography from the 1950s onward; the authors always point out when the developments in the field occurred and give the resulting texts that built upon those developments up to the present day, giving a nice historical context. If a graduate student or professor wants a full taste of the spatial statistics literature—where it has been, where it is, and where it still needs to go—this is probably one of the best books they could pick up. In many ways, readers of Hierarchical Modeling and Analysis for Spatial Data would simultaneously be readers of the spatial statistics literature as well.

There are many books on spatial statistics, but one reference persists: Noel Cressie’s now-classic textbook Statistics for Spatial Data—a favorite among spatial statistics course instructors. Both books are very comprehensive reviews of spatial statistics, but Hierarchical Modeling and Analysis for Spatial Data may be less intimidating than Cressie’s book in that it is about half the size while still thorough and substantive. This book provides a similar amount of rigor while taking advantage of recent advancements in theory and computation. Indeed, the authors acknowledge that they have had the advantage of having references like Cressie’s book to build on. We find this book to give a much more applied perspective with better computational tools, and thus believe it to be more accessible to a wider audience.

We recommend this book to anyone who seriously wants to start being involved in spatial statistics. This is a great book for both professors and practitioners, but the authors of this review can also speak from experience that this is an excellent book for first-year graduate students who want to be introduced to the spatial statistics field.

Zach J. Branson, Luis F. Campos, and Lukew.Miratrix

Harvard University

Introduction to High-Dimensional Statistics.

Christophe Giraud. New York: Chapman & Hall/CRC Press, 2014, xv + 255 pp., $69.95(H), ISBN: 978-1-48-223794-8.

The information era has witnessed an explosion in the collection of data that contain potentially useful information for a wide range of applications such as biology, sociology, pattern recognition, marketing, and finance. As a result of this inflation, statisticians have developed a new set of tools that combine fundamental statistical concepts with new and profound ideas. This set of problems and tools is broadly referred to as high-dimensional statistics.

The book Introduction to High-Dimensional Statistics by Christophe Giraud succeeds singularly at providing a structured introduction to this active field of research. It describes a statistical pipeline, where statistical principles enable the development of new methods, which, in turn, require a new mathematical analysis.

Most of “classical statistics” focus on situations, where the number p of parameters of a model is much smaller than the number n of observations. As a result, asymptotic results where $n → ∞$ and p is fixed prevailed in the 20th century, relying on results such as the law of large number or the central limit theorem for example. In high-dimensional statistics, it is often the case that $p ≫ n$ so that traditional asymptotic results no longer provide a theoretical explanation for the behavior of a statistical procedure. Several approaches can be found in the literature and this book follows a preponderant trend that consists in replacing sharp asymptotic statements such as “consistency” or “asymptotic normality” with finite sample risk bounds. Unfortunately, without further assumptions, such bounds are typically too large to be informative when $p ≫ n$. In this context, the effectiveness of high-dimensional statistical methods has relied on structural assumptions. One such assumption that Giraud describes in great detail is sparsity.

The sparsity assumption essentially postulates that there exists a much smaller submodel that can explain the data quite well. Finding this submodel falls in the general framework of model selection and can be achieved using penalization. A systematic finite sample analysis of these techniques was developed in the nineties under a very general setup devoid of any computational considerations. Chapter 2 revisits this general theory and instantiates it on several variations of sparsity assumption. A recent alternative to model selection, called aggregation, is explored in Chapter 3. It leads to statistical procedures that have optimality properties similar to model selection procedures but that are quite different in nature. Unfortunately, in the context of sparsity, both approaches require prohibitively high computation.

The statistical principles exploited in Chapters 2 and 3 do not represent a major break from the finite sample analysis of classical statistical procedures such as model selection in (low-dimensional) linear regression. A salient feature of high-dimensional statistics is the appearance of computationally efficient methods with provable guarantees as opposed to heuristics such as stepwise regression for example. The popular Lasso estimator employed in linear regression is one such example. Chapter 4 carries out detailed mathematical analysis of the prediction performance of this estimator. In particular, this analysis surveys the key ingredients of the proof in such a way that it is completely demystified. Moreover, the chapter explores several state-of-the-art algorithms to compute the Lasso estimator and points to R implementations. It is worth mentioning that this chapter focuses exclusively on prediction performance and leaves other important questions such as variable selection and parameter estimation as guided exercises.

The Lasso estimator, like many other estimators employed in high-dimensional statistics, requires tuning one or more parameters that significantly affect their performance. Procedures for choosing these turning parameters, including the celebrated “cross-validation” method, are presented mostly without proofs in Chapter 5, together with a thorough analysis of the square-root Lasso (a popular twist on the Lasso that can be tuned without knowing the variance of the noise).

More recently, high-dimensional statistics have witnessed the rise of problems where the parameter of interest is not a vector but a matrix or a graph. In this context, surprisingly similar techniques apply not only under the sparsity assumption but also under the assumption that the matrix of interest has low rank, which turns out to be natural in this context. This is perhaps the first book to offer a clear and detailed treatment of matrix estimation in the context of multivariate regression. The treatment of graphical models is more superficial due to extra technicalities, but the methods are clearly defined and motivated in view of the earlier chapters on sparse linear regression.

The rest of the book departs somewhat from the first chapters to describe other issues arising in high-dimensional statistics thus providing a bit of diversity to the reader interested in exploring other topics. On the one hand, Chapter 8 is devoted to multiple testing with emphasis on the false discovery rate (FDR). The proofs in this chapter are much simpler than the first part of the book since they are quite different in nature and no connection with the results of the previous chapters is made. On the other hand, Chapter 9 covers supervised classification, a core topic in statistical learning theory. The treatment is fairly classical with upper bounds on the excess risk using fundamental tools from empirical process theory such as symmetrization and VC dimension. This chapter also provides a fairly detailed treatment of risk convexification, a technique that can be used to provide a unified framework to several classical machine learning methods such as boosting and support vector machines.

A striking aspect of this book is the omnipresence of computational considerations across chapters. The author carefully points to potential implementations, R packages and algorithmic details that have now become inherent to modern high-dimensional statistical research. Beyond a unified and cohesive treatment, Giraud also offers informative and fairly comprehensive bibliographical notes that point to the main results of the field as well as connected work. Once the subject has been mastered, the reader is invited to attempt to solve some of the numerous exercises provided at the end of each chapter. These exercises provide detailed guidelines on how to derive key results from the recent literature and are one of the best features of this book. Put together, the exercises amount to the equivalent of another book and provide a lot of insight on how the core concepts encountered in the main text extend to other problems.

This book is not a global overview of all the aspects of high-dimensional statistics and focuses primarily on prediction performance, much in the spirit of statistical learning theory. However, it is arguably the most accessible overview yet published of the mathematical ideas and principles that one needs to master to enter the field of high-dimensional statistics. Indeed, several years have passed since the publication of Statistics for High-Dimensional Data by Peter Bühlmann and Sara van de Geer (2001), which is widely considered as the main reference on the theory of high-dimensional statistics. These years have allowed Giraud to distill the core elements of the literature and simplify some of the arguments so that Introduction to High-Dimensional Statistics can serve as a gentle introduction to the more advanced text. This feeling is reinforced by an engaging introduction (Chapter 1) that brings forward the key challenges associated with high-dimensional data and a nice account of useful probabilistic inequalities in the Appendix. It should be recommended to anyone interested in the main results of current research in high-dimensional statistics as well as anyone interested in acquiring the core mathematical skills to enter this area of research.

Philippe Rigollet

Massachusetts Institute of Technology

Machine Learning: A Probabilistic Perspective.

Kevin P. Murphy. Cambridge, MA: MIT Press, 2012, xxix + 1067 pp., $95.00 (H), ISBN: 978-0-26-201802-9.

This is my favorite machine learning book, where I include “statistical learning,” “data mining,” and other such terms in the category. Other well-known texts in this area include The Elements of Statistical Learning by Hastie2009, Tibshirani, and Friedman and Pattern Recognition and Machine Learning by Bishop2007.

The fundamentally amazing thing about Murphy’s book is that it actually lives up to its subtitle: “A Probabilistic Perspective.” The book takes the view that by adopting this perspective, it can cover a lot of ground and still be intuitive and applied while still covering the details of the ideas and algorithms. Thus, while the book is “big” it is very approachable. Throughout the book the figures are carefully thought out, extremely helpful in understanding the ideas, and attractive. This book is my “go-to” reference; if I do not know a topic I check Murphy first.

The first chapter does an admirable job of giving the reader an overview of the basic ideas and challenges of Machine Learning. Chapters 2–6 review basic modeling and inference concepts. A distinguishing feature of the book is that both the Bayesian and frequentist approaches for methods and models are discussed, and are given equal footing. Those with a solid background in statistics will find it useful to consult this material to learn the notation used later in the book. It is a bit embarrassing how often I find it useful to use these early chapters to review basic stuff I have not come across for a while. It is hard for me to assess what it would be like to learn the ideas from scratch using Chapters 2–6, but every effort is made to give simple examples and intuitive explanations.

Chapters 7–9 cover the basic linear and “linear-like” statistical models: linear regression, logistic regression, and generalized linear models. While these chapters start with the assumption that you know nothing and hence review the basic concepts, topics are discussed from a modern perspective. For example, a section on Ridge regression includes a subsection titled “Regularization effects of big data” and there is a section “Online learning and stochastic optimization” in the chapter on logistic regression. The chapter on logistic regression also includes a section “Generative vs. Discriminative classifiers” in which the pros and cons of modeling $y|x$ versus $(x|y, y)$ for classification are discussed. Throughout the book, there is a real effort to discuss the overarching themes of the models and how the ideas play out in practice.

While much valuable material is in Chapters 1–9, the book really gets going in Chapters 10, 11, and 12 that cover directed graphical models, mixture modeling, and latent linear models. Chapter 13 on “Sparse linear model” captures a basic strength of the book: the penalized optimization approach is nicely discussed as well as the hierarchical Bayesian modeling approach.

The rest of the book is a tour de force discussion of a remarkably broad set of Machine Learning tools from support vector machines to deep learning. Given the basic philosophy of the book, particularly useful and impressive chapters cover Markov models (HMM and State-Space) and Graphical Models. A set of chapters of graphical models discuss both the structure and the estimation of the models. It is very valuable to have a complete treatment of these topics.

Two chapters treat Monte Carlo inference (including Markov chain Monte Carlo, MCMC), and two more chapter are devoted to variational inference. A chapter I found particularly helpful is on “Latent variable models for discrete data,” which emphasizes models for text data. The final chapter is on “Deep learning.”

In summary, this book actually delivers on using a “probabilistic perspective” to make a broad range of topics accessible. Chapters are structured so that you can get the basic idea very quickly and then read on for more depth. Important and interesting examples of application domains (simple and complex) are given throughout with useful references. It is an invaluable reference.

Robert E. Mcculloch

University of Chicago

Multiple Factor Analysis by Example Using R.

Jérôme PagéS. New York: Chapman & Hall/CRC Press, 2014, xiv + 257 pp., $89.95 (H), ISBN: 978-1-48-220547-3.

Multiple Factor Analysis by Example Using R provides a comprehensive overview of the eponymous method, as well as several related analysis tools, across 10 chapters and a mathematical appendix. Each chapter, punctuated with a lovely piece of calligraphic notation (except for the first and third chapters, sadly), clearly and concisely outlines either an application of multiple factor analysis (MFA; “Weighting Groups of Variables,” “Comparing Clouds of Partial Individuals”), or a related method (“Principal Components Analysis,” “Multiple Correspondence Analysis”). Almost every chapter, as well, concludes with several full pages of R instruction, using both the “R Commander” GUI and classic command-line R. The code primarily implements the author’s own CRAN-supported package “FactoMineR,” a large contribution on its own, containing 79 unique documentation entries.

While occasionally overreliant on notation in lieu of providing intuition, by and large the text’s brevity is a strength. There are very few formal proofs. Instead, there is a pleasant abundance of figures, tables, and three-dimensional (3D) plots. For example, in Chapter 1, rather than deriving the principal components analysis optimization function under either the preservation or reconstruction paradigms, the author instead provides intuition of and defines notation for the quantities of interest, then skillfully produces diagrams to clarify the geometric logic behind dimensionality reduction.

The text builds toward the use of MFA for “mixed data,” datasets with both quantitative and qualitative variables, as its capstone method. Note that while the author never fully explains the difference, quantitative and qualitative variables seem to be code for ordinal and categorical variables. The first three chapters cover what might be called fundamentals, including more traditional factorial methods such as principal components analysis (PCA) and multiple correspondence analysis (MCA), but also a more general method for mixed data called factorial analysis for mixed data (FAMD). The fourth chapter introduces MFA in the context of grouping variables, and in the following three chapters, the book explains additional features and applications of the core approach. The eighth, ninth, and tenth chapters extend MFA to include mixed data and hierarchical variable structures. The final chapter, largely a mathematical appendix spanning fewer than 10 pages, covers matrix algebra and the geometric interpretations of multidimensional vectors.

Chapter 1, covering principal components analysis, begins reasonably enough: it introduces reasons for using PCA to study the quality of students with multiple letter grades across various subjects. Rather than introducing PCA from either the reconstruction perspective or the variance preservation perspective, the author speaks geometrically, in terms of “clouds of individuals” and “clouds of variables,” the inertia of these clouds, and the distances between them. This notation and terminology holds throughout the text. In concluding Chapter 1, the author dedicates six pages to R code and output, primarily canned functions included in the “FactoMineR” package. Subsequent chapters generally follow this structure, although several include no code.

While each chapter is useful in its own right, this book really shines in the four chapters that focus on multiple factor analysis. MFA is laid out lucidly, with detailed explanations of its desirable qualities. MFA is, at its heart, a method used to explore datasets in which observations are described by groups of quantitative, qualitative, or mixed data, which it does by weighting the variables separately or in groups. In this way, it is related to almost all other factorial methods, a point the author delights in making frequently; rarely does another method arise as other than a special case of, or an inferior product to, multiple factor analysis. In Chapter 6, the author illustrates how MFA can be thought of as a specific form of canonical analysis, in which two groups of variables are taken in linear combinations so as to maximize the correlation between the two combined factors. In the concluding remarks to that chapter, the author discusses how understanding MFA as a variant of canonical analysis facilitates interpreting MFA outputs: “These [canonical correlation] coefficients are said to be canonical in MFA. Consulted at the beginning of an interpretation, they guide the user by suggesting the type of each factor (either common to all groups, or to some of them, or specific to just one group).”

A weak point of this text, frankly, is that while its core methods are useful and well explained, its examples tend not to be compelling. The modal data analysis example is a dataset of chemical and physical properties of several brands of orange juice. The final two substantive chapters are on Procrustes analysis and hierarchical MFA: The former focuses on comparing the shape of groups, in this case individuals or variables, by optimal scaling and translating; the latter extends MFA to allow for nested hierarchies of variables. These methods are both rich and highly applicable to questions that statisticians may be interested in answering; yet, the author applies these two methods only to datasets related to napping (the R code describes this dataset as “napping with white wines from the Loire Valley”) and orange juice. While statistics texts do not necessarily need to teach interesting tools and solve interesting problems at the same time, a text with as little mathematical elaboration as this one is clearly directed at an audience interested in applying these tools specifically, and I would have a greater understanding of, and interest in applying, such factorial methods if I had some idea of substantive problems to which they might be applied.

The structure of the text suggests that MFA is a superior alternative to more traditional techniques, but at no point does the author state this. PCA and MCA are both introduced prior to MFA, but the author never satisfactorily explains why the latter should be used instead of the former. Admittedly, showing that MFA outperforms PCA or MCA would be a formidable task, as there is no obvious evaluation metric for factorial methods in general. But given the amount of ink dedicated to MFA, when there are clearly so many other types of factorial methods to explore, it would behoove the author to explain his choice.

While much code is provided, the book is unfortunately not fully reproducible: very little of the data necessary for the sample analyses that conclude each chapter is included in the R package, or the author’s additional package, “SensoMineR.” The book’s introduction points to the Agrocampus Ouest Applied Mathematics Department website for the remainder, though after some time spent navigating with the aid of Google Translate, I was unable to locate those datasets. Luckily, those examples for which data are included in the “FactoMineR” package are usually labeled as such, so readers interested in following along with code can know where to focus their attention.

In practice, this text should prove useful to any researcher interested in exploring dimension reduction techniques, especially with applications to qualitative or mixed data. It deftly avoids a major pitfall common to books focused on relatively narrow methods whereby naive readers find themselves competent in using the tools or replicating an analysis with no real comprehension. Finally, the text’s fluid integration with an R package, useful in its own right and independent of the text, is greatly to its benefit.

Aaron R. Kaufman

Harvard University

Nonlinear Time Series: Extreme Events and Integer Value Problems.

Kamil Feridun Turkman, Manuel González Scotto, and Patrícia De Zea Bermudez. Berlin: Springer International Publishing, 2014, xii+245 pp., $109.00 (H), ISBN: 978-3-31-907027-8.

Nonlinear time series represents a very broad area within statistics and econometrics, and research in this field has grown rapidly in recent years. With regard to its empirical applications, nonlinear time series models have increasingly become a valid alternative to model processes that depict high variability and heavy tails. These processes are found in a variety of fields, ranging from economics to telecommunications. In particular, the field of financial econometrics has profited from nonlinear models as a way to model higher-order moments of financial returns such as, for instance, the use of the GARCH family of models to represent conditional heteroscedasticity. Inference and estimation of nonlinear time series models have always been major drawbacks when compared to linear processes, but the recent computational and theoretical advances have made these models much more attractive so that researchers and practitioners can now include them in their everyday toolboxes. The theoretical treatment of nonlinear models is also more involved when compared to linear models, with issues such as invertibility and estimation playing an important role. Therefore, a book that reviews this literature and includes up-to-date references is highly welcome.

Nonlinear Time Series by Kamil Feridun Turkman, Manuel González Scotto, and Patrícia de Zea Bermudez aims to cover a wide range of topics in nonlinear time series analysis. Hence, the book intends to be a primary source of information rather than a rigorous and deep literature review, distinguishing it from well-established books such as Tong (1990) and Fan and Yao (2003). My overall opinion is that the authors accomplish this goal. A drawback is that the reader may wish for a deeper and more rigorous treatment of the topics. Hence, the Nonlinear Time Series book cannot be seen as a substitute for Tong (1990) and Fan and Yao (2003). Instead, it should be considered as a book where a reader could begin study.

The book is divided into five chapters. The first chapter motivates the importance of nonlinear time series and introduces relevant datasets and nonlinear models that are revisited in the subsequent chapters. Chapter 2 discusses some probabilistic aspects of nonlinear time series and provides an overview of parametric, semiparametric and nonparametric models. This chapter is particularly interesting for a reader who has a good background in probability theory and lacks a broad view on nonlinear models and their applications. By navigating through models that are adopted in different fields, this chapter successfully introduces nonlinear time series models and their applications to a diverse audience. Moreover, the discussion of the properties of linear and nonlinear models is extremely useful, particularly for economics students who have attended the classical econometrics courses and are usually much more familiar with linear time series models. In fact, this chapter sets the stage for the entire book and, as a consequence, the reader may feel that a few more pages would have been useful.

The third chapter effectively discusses extreme events, shedding light on the connection between nonlinear models and heavy tails. I find the discussion pleasant to read, but the exposition is heavily based on a succession of definitions and theorems. As the audience could be broad and heterogeneous, I would expect to also see empirical examples as tail behavior plays a crucial role in financial econometrics and other fields. Nevertheless, the reader is offered a good review on the extremal properties of linear and nonlinear models.

Chapter 4 discusses inferential methods for nonlinear models. The first part of this chapter focuses on tests that aim to distinguish between linear and nonlinear models. The second part of the chapter examines different estimation techniques that can be adopted to deal with nonlinear models. The authors provide a brief overview of the following methods: least squares, maximum likelihood, estimating functions, composite likelihood, and Bayesian methods. The chapter successfully gives an outline of these different techniques, pointing the reader to the appropriate literature. Finally, the last part of this chapter reviews estimation of the GARCH family of models. This is a very interesting discussion as the authors do not only focus on covering the asymptotic theory of covariance stationary GARCH models with finite fourth moment, but go on to briefly discuss the cases of infinite fourth moment, nonstationary GARCH models, and Bayesian inference. After finishing Chapter 4, the reader will have a good grasp of the different methodologies available and, more importantly, a valuable set of references for gaining a deeper understanding of their theoretical properties.

Finally, Chapter 5 discusses integer-valued time series models based on thinning operators. This chapter joins Fokianos (2012) as another comprehensive review on this literature. The reader is offered a review on model properties, parameter estimation, and model selection. Compared to the previous chapters, Chapter 5 examines the topics more in depth and is therefore more self-contained.

With regard to its use as teaching material, the book is not formatted as a textbook. For instance, it does not include an Appendix, exercises, subject index, or examples of computer code. An Appendix that introduced the preliminary probabilistic and statistical results used in the book would benefit many readers (mostly graduate students who usually have different backgrounds). In particular, economics students often require a few lectures reviewing these concepts. Nonetheless, this book could be used for a graduate course covering selected topics in nonlinear time series, where it is used either as an initial reference or as supplementary literature. Combining it with Fan and Yao (2003) or with selected articles seems to be the most natural choice. Specifically, Chapter 5 could stand as the primary literature for a short course (topic) on models for integer-valued time series.

Gustavo F. Dias

Aarhus University and CREATES

Time Series with Mixed Spectra.

Ta-Hsin Li. New York: Chapman & Hall/CRC Press, 2013, x + 670 pp., $83.95(H), ISBN: 978-1-58-488176-6.

This book is a comprehensive treatment of modeling and analysis of time series data with mixed spectra. Such data are encountered in many scientific areas, where the signal contains a number of seasonality components (e.g., daily, monthly, annual) but is buried in correlated noise. There have been many advances on modeling such time series data. This book is an impressive collection of these results and a number of which were actually the authors own contributions to the literature.

This book is most useful as a research monograph. It is a must-read especially for a novice researcher to this area. It masterfully integrates the most significant advances in the literature. The book carefully treats both real-valued and complex-valued time series. The latter has received less attention in the literature but is slowly attracting more attention in functional magnetic resonance imaging analysis. Moreover, the organization is cohesive and the writing style appeals to electrical engineers and statisticians. The book strives to present these ideas with intuition at the start of each chapter and then concludes with theoretical results (complete with proofs).

The book begins with a lucid introduction on periodicity, sampling, and aliasing. These concepts are not emphasized enough in statistics time series courses and the author is commended for taking the effort to clearly deliver these ideas. In my opinion, the most notable chapters in this book are Chapter 2 (on the foundations of spectral analysis), Chapter 5 (on Linear regression analysis), and Chapter 6 (on Fourier analysis). Chapter 2 presents the foundations of spectral analysis, covering the parameterization of sinusoids, the stochastic representation of stationary time series with the Fourier waveforms, and the formal definition of the spectrum. This chapter nicely complements the standard time series textbooks such as Brockwell and Davis (1991), Brillinger (2001), and Shumway and Stoffer (2010). The delivery of the foundational ideas of spectral analysis is appealing especially to a student who understands the notions of a basis and of representing random vectors (time series) with the Fourier basis. Chapter 5 treats the modeling of time series in terms of sinusoids as predictors where such oscillations have fixed but possibly unknown frequencies. In this case, the amplitudes are treated as fixed parameters that have to be estimated from the data. I see this chapter as a first step toward understanding Fourier regression with random coefficients (Cramer representation). Chapter 6 discusses the classical periodogram analysis approach to identifying the sinusoids and estimation of the underlying noise spectra. Chapter 3 is also noteworthy as it covers the Cramer–Rao lower bound which is a highly specialized topic. It is glossed over in the standard time series texts; it is less prominent in the statistics time series literature compared to signal processing.

The book can serve as a primary textbook for a special topics course on this area and also a supplementary textbook for a time series course with an emphasis on spectral analysis especially because the concept of mixed spectra is often not emphasized in standard spectral analysis-oriented textbooks such as Brillinger (2001) and Shumway and Stoffer (2010). In fact, a ten-week quarter course on spectral analysis could be taught based on the following chapters: 1,2,4,5,6,7,8,9. However, exercises will have to be supplemented by the instructor. Perhaps if the author is planning on future improvements, he might consider adding exercises and R codes following the model of Shumway and Stoffer (2010) which wrote R codes for the specific text examples and made these available online. In my own experience, these codes have served as an indispensable tool for both the students and the instructors.

Hernando Ombao

University of California, Irvine