Non-Parametric Econometrics

Non-Parametric Econometrics, by I. Ahamada and E. Flachaire, New York, Oxford University Press, 2010, xiv+161 pp., £35.00 or US$55.39 (hardback), ISBN 978-0-19-957800-9

This book focuses on nonparametric techniques, which offer greater flexibility in modelling than their parametric counterparts. The book begins by introducing kernel techniques to estimate data density. The smoothing performance of a kernel estimator is determined by a bandwidth. Amongst many bandwidth selection methods, the authors describe rules of thumb, the plug-in method and cross-validation. Although the authors have mentioned multivariate density estimation, they do not discuss how to select bandwidth for multivariate data in any great detail.

Equipped with the tools of kernel techniques, the authors apply them to a regression setting with scalar responses and vector predictors. Nadaraya–Watson kernel regression is a special case of local polynomial regression, where the latter overcomes the bias problem and boundary effect.

Extending from classical ordinary least-squares regression, spline regression is another popular smoothing technique, where smoothness is governed by a smoothing parameter λ. The selection of smoothing parameter, spline basis function and the number of knots are discussed. By using penalised spline regression, a user has to choose only the optimal smoothing parameter with the default cubic spline bases and a large number of knots.

Although spline-type bases have compact support, they are not orthogonal. This motivates the development of wavelets. Not only are they orthogonal with compact support, but they also have the property of multiresolution, which allows us to see the finest details of the estimated function without losing sight of its global characteristics. The wavelet basis consists of a ‘father’ wavelet capturing the global behaviour and ‘mother’ wavelets capturing the different levels of local behaviour. The authors discuss two popular families of wavelet basis functions, the choice of filters and thresholds, and their performance.

The authors further demonstrate the use of nonparametric techniques in semi-parametric regression models. While a parametric model requires a correct specified distributional form, a nonparametric model suffers from the so-called “curse of dimensionality”. Because of that, semi-parametric regression (such as the partial linear model and the single-index model) has recently received increasing attention.

Building upon semi-parametric regression, the authors introduce finite mixture models. In density estimation, finite mixture models are able to estimate any density function. Finite mixture models have been widely applied to classification and discrimination problems, where a population consists of many different groups.

The only weakness of the text is the limited range of code for the examples used throughout the book. I hope that the authors could build an package that allows other users to reproduce their analyses.

Overall, I enjoyed reading this book and thought that it gives a concise review into nonparametric techniques. It is a clearly written and well-structured book for a diverse range of audiences, like econometricians and statisticians. It serves perfectly as a practical reference for researchers and graduate students with an interest in nonparametric techniques. A broader review on other nonparametric techniques, such as bootstrap and jackknife, is given in Hall 1.

http://dx.doi.org/02664763.2011.575999