Advanced search
Publication Cover
Journal of the American Statistical Association Volume 105, 2010 - Issue 490
Submit an article Journal homepage
673
Views
71
CrossRef citations to date
0
Altmetric
Theory and Methods

Simultaneous Confidence Bands for Penalized Spline Estimators

Tatyana Krivobokova Tatyana Krivobokova is Associate Professor, Courant Research Center PEG and Institute for Mathematical Stochastics, Georg August Universität Göttingen, Platz der Göttinger Sieben 3, 37073 Göttingen, Germany . Thomas Kneib is Professor, Mathematics Department, Carl von Ossietzy Universität Oldenburg, 26111 Oldenburg, Germany. Gerda Claeskens is Professor, ORSTAT and Leuven Statistics Research Center, Katholieke Universiteit Leuven, Naamsestraat 69, 3000 Leuven, Belgium. The authors thank the editor, the referees, and Dr. Tatiyana Apanasovich for constructive remarks. They also thank Manuel Wiesenfarth for the substantial improvements to the R program used for the Bayesian confidence bands. The first author acknowledges the support of the German Research Foundation (Deutsche Forschungsgemeinschaft) as part of the Institutional Strategy of the University of Göttingen.
,
Thomas Kneib Tatyana Krivobokova is Associate Professor, Courant Research Center PEG and Institute for Mathematical Stochastics, Georg August Universität Göttingen, Platz der Göttinger Sieben 3, 37073 Göttingen, Germany . Thomas Kneib is Professor, Mathematics Department, Carl von Ossietzy Universität Oldenburg, 26111 Oldenburg, Germany. Gerda Claeskens is Professor, ORSTAT and Leuven Statistics Research Center, Katholieke Universiteit Leuven, Naamsestraat 69, 3000 Leuven, Belgium. The authors thank the editor, the referees, and Dr. Tatiyana Apanasovich for constructive remarks. They also thank Manuel Wiesenfarth for the substantial improvements to the R program used for the Bayesian confidence bands. The first author acknowledges the support of the German Research Foundation (Deutsche Forschungsgemeinschaft) as part of the Institutional Strategy of the University of Göttingen.
&
Gerda Claeskens Tatyana Krivobokova is Associate Professor, Courant Research Center PEG and Institute for Mathematical Stochastics, Georg August Universität Göttingen, Platz der Göttinger Sieben 3, 37073 Göttingen, Germany . Thomas Kneib is Professor, Mathematics Department, Carl von Ossietzy Universität Oldenburg, 26111 Oldenburg, Germany. Gerda Claeskens is Professor, ORSTAT and Leuven Statistics Research Center, Katholieke Universiteit Leuven, Naamsestraat 69, 3000 Leuven, Belgium. The authors thank the editor, the referees, and Dr. Tatiyana Apanasovich for constructive remarks. They also thank Manuel Wiesenfarth for the substantial improvements to the R program used for the Bayesian confidence bands. The first author acknowledges the support of the German Research Foundation (Deutsche Forschungsgemeinschaft) as part of the Institutional Strategy of the University of Göttingen.
Pages 852-863 | Received 01 Mar 2009, Published online: 01 Jan 2012

Citations (71)

Keep up to date with the latest research on this topic with citation updates for this article.

Subscribe to citation updates

Read on this site (11)

Shan Yu, Guannan Wang, Li Wang, Chenhui Liu & Lijian Yang. (2020) Estimation and Inference for Generalized Geoadditive Models. Journal of the American Statistical Association 115:530, pages 761-774.
Read now
Kenneth Harttgen, Stefan Lang, Judith Santer & Johannes Seiler. (2020) Modelling Under-Five Mortality through Multilevel Structured Additive Regression with Varying Coefficients for Asia and Sub-Saharan Africa. The Journal of Development Studies 56:2, pages 401-430.
Read now
Aurore Delaigle, Wei Huang & Shaoke Lei. (2020) Estimation of Conditional Prevalence From Group Testing Data With Missing Covariates. Journal of the American Statistical Association 115:529, pages 467-480.
Read now
Francis K. C. Hui, C. You, H. L. Shang & Samuel Müller. (2019) Semiparametric Regression Using Variational Approximations. Journal of the American Statistical Association 114:528, pages 1765-1777.
Read now
Lin Zhang, Veerabhadran Baladandayuthapani, Hongxiao Zhu, Keith A. Baggerly, Tadeusz Majewski, Bogdan A. Czerniak & Jeffrey S. Morris. (2016) Functional CAR Models for Large Spatially Correlated Functional Datasets. Journal of the American Statistical Association 111:514, pages 772-786.
Read now
K. De Brabanter, Y. Liu & C. Hua. (2016) Convergence rates for uniform confidence intervals based on local polynomial regression estimators. Journal of Nonparametric Statistics 28:1, pages 31-48.
Read now
Nadja Klein, Thomas Kneib & Stefan Lang. (2015) Bayesian Generalized Additive Models for Location, Scale, and Shape for Zero-Inflated and Overdispersed Count Data. Journal of the American Statistical Association 110:509, pages 405-419.
Read now
Manuel Wiesenfarth, Carlos Matías Hisgen, Thomas Kneib & Carmen Cadarso-Suarez. (2014) Bayesian Nonparametric Instrumental Variables Regression Based on Penalized Splines and Dirichlet Process Mixtures. Journal of Business & Economic Statistics 32:3, pages 468-482.
Read now
Huaihou Chen, Yuanjia Wang, Myunghee Cho Paik & H. Alex Choi. (2013) A Marginal Approach to Reduced-Rank Penalized Spline Smoothing With Application to Multilevel Functional Data. Journal of the American Statistical Association 108:504, pages 1216-1229.
Read now
Zhongyuan Yu, Nicoleta Serban & WilliamB. Rouse. (2013) The Demographics of Change: Enterprise Characteristics and Behaviors that Influence Transformation. Journal of Enterprise Transformation 3:4, pages 285-306.
Read now
Manuel Wiesenfarth, Tatyana Krivobokova, Stephan Klasen & Stefan Sperlich. (2012) Direct Simultaneous Inference in Additive Models and Its Application to Model Undernutrition. Journal of the American Statistical Association 107:500, pages 1286-1296.
Read now

Articles from other publishers (60)

Katarzyna Reluga, María‐José Lombardía & Stefan Sperlich. (2022) Simultaneous inference for linear mixed model parameters with an application to small area estimation. International Statistical Review 91:2, pages 193-217.
Crossref
Roger Koenker. (2023) Hotelling tubes, confidence bands and conformal inference. Empirical Economics 64:6, pages 2757-2769.
Crossref
Joanna Boland, Donatello Telesca, Catherine Sugar, Michele Guindani, Shafali Jeste, Abigail Dickinson, Charlotte DiStefano & Damla Şentürk. (2023) Central Posterior Envelopes for Bayesian Functional Principal Component Analysis. Journal of Data Science, pages 1-20.
Crossref
Esra Kürüm, Danh V. Nguyen, Sudipto Banerjee, Yihao Li, Connie M. Rhee & Damla Şentürk. (2022) A Bayesian multilevel time‐varying framework for joint modeling of hospitalization and survival in patients on dialysis. Statistics in Medicine 41:29, pages 5597-5611.
Crossref
Methsarani Premathilaka & Rong Liu. (2022) Simultaneous confidence bands for nonparametric regression with equal cluster size. Stat 11:1.
Crossref
Yihao Li, Danh V. Nguyen, Esra Kürüm, Connie M. Rhee, Sudipto Banerjee & Damla Şentürk. (2022) Multilevel varying coefficient spatiotemporal model. Stat 11:1.
Crossref
John Shamshoian, Damla Şentürk, Shafali Jeste & Donatello Telesca. (2022) Bayesian analysis of longitudinal and multidimensional functional data. Biostatistics 23:2, pages 558-573.
Crossref
Jiangyan Wang, Lijie Gu & Lijian Yang. (2022) Oracle-efficient estimation for functional data error distribution with simultaneous confidence band. Computational Statistics & Data Analysis 167, pages 107363.
Crossref
Fabian J.E. Telschow & Armin Schwartzman. (2022) Simultaneous confidence bands for functional data using the Gaussian Kinematic formula. Journal of Statistical Planning and Inference 216, pages 70-94.
Crossref
Jeong Eun Lee & Geoff K. Nicholls. (2021) Tree based credible set estimation. Statistics and Computing 31:6.
Crossref
Nadja Klein, Manuel Carlan, Thomas Kneib, Stefan Lang & Helga Wagner. (2021) Bayesian Effect Selection in Structured Additive Distributional Regression Models. Bayesian Analysis 16:2.
Crossref
Stewart Curry & Nicoleta Serban. (2021) Accounting for uncertainty in policy decision making: Improving access to pediatric dental care. Health Services Research 56:2, pages 214-224.
Crossref
Lijie Gu, Suojin Wang & Lijian Yang. (2021) Smooth simultaneous confidence band for the error distribution function in nonparametric regression. Computational Statistics & Data Analysis 155, pages 107106.
Crossref
Nicolò Margaritella, Vanda Inácio & Ruth King. (2020) Parameter clustering in Bayesian functional principal component analysis of neuroscientific data. Statistics in Medicine 40:1, pages 167-184.
Crossref
Johannes Seiler, Kenneth Harttgen, Thomas Kneib & Stefan Lang. (2021) Modelling children's anthropometric status using Bayesian distributional regression merging socio-economic and remote sensed data from South Asia and sub-Saharan Africa. Economics & Human Biology 40, pages 100950.
Crossref
Takuma Yoshida. (2019) Simultaneous confidence bands for extremal quantile regression with splines. Extremes 23:1, pages 117-149.
Crossref
Nicoleta Serban. 2020. Healthcare System Access. Healthcare System Access 61 97 .
Roberto Rivera & Wolfgang Rolke. (2019) Modeling excess deaths after a natural disaster with application to Hurricane Maria. Statistics in Medicine 38:23, pages 4545-4554.
Crossref
Luo Xiao. (2019) Asymptotic theory of penalized splines. Electronic Journal of Statistics 13:1.
Crossref
Alexander BauerFabian ScheiplHelmut KüchenhoffAlice-Agnes Gabriel. (2018) An introduction to semiparametric function-on-scalar regression. Statistical Modelling 18:3-4, pages 346-364.
Crossref
Monica Gentili, Pravara Harati, Nicoleta Serban, Jean O'Connor & Julie Swann. (2017) Quantifying Disparities in Accessibility and Availability of Pediatric Primary Care across Multiple States with Implications for Targeted Interventions. Health Services Research 53:3, pages 1458-1477.
Crossref
Leonardo Lancia & Benjamin Rosenbaum. (2018) Coupling relations underlying the production of speech articulator movements and their invariance to speech rate. Biological Cybernetics 112:3, pages 253-276.
Crossref
Rita Diana. (2018) Smoothing spline in multivariable semiparametric regression through fully bayesian approach. Model Assisted Statistics and Applications 13:2, pages 123-132.
Crossref
Peter Pütz & Thomas Kneib. (2017) A penalized spline estimator for fixed effects panel data models. AStA Advances in Statistical Analysis 102:2, pages 145-166.
Crossref
Manuel Vonrüti, Aleksandar Spasojevic, Nils Nölke, Thomas Kneib & Christoph Kleinn. (2017) Comparing canopy leaf temperature of three Central European tree species based on simultaneous confidence bands for penalized splines. Environmental and Ecological Statistics 24:3, pages 385-398.
Crossref
Thomas Kopp, Bernhard Brümmer, Zulkifli Alamsyah & Raja Sharah Fatricia. (2017) Welfare implications of intertemporal marketing margin manipulation. British Food Journal 119:8, pages 1656-1671.
Crossref
Wiebke Hammerschmidt, Holger Sennhenn-Reulen & Annekathrin Schacht. (2017) Associated motivational salience impacts early sensory processing of human faces. NeuroImage 156, pages 466-474.
Crossref
David Degras. (2017) Simultaneous confidence bands for the mean of functional data. Wiley Interdisciplinary Reviews: Computational Statistics 9:3, pages e1397.
Crossref
Junshu BaoTimothy HansonGarnett P. McMillanKristin Knight. (2017) Assessment of DPOAE test-retest difference curves via hierarchical Gaussian processes. Biometrics 73:1, pages 334-343.
Crossref
Xiaolei Lu & Satoshi Kuriki. (2017) Simultaneous confidence bands for contrasts between several nonlinear regression curves. Journal of Multivariate Analysis 155, pages 83-104.
Crossref
Elmar Spiegel, Fabian Sobotka & Thomas Kneib. (2017) Model selection in semiparametric expectile regression. Electronic Journal of Statistics 11:2.
Crossref
Ashley D. Holland. (2017) Penalized spline estimation in the partially linear model. Journal of Multivariate Analysis 153, pages 211-235.
Crossref
Roland Langrock, Thomas Kneib, Richard Glennie & Théo Michelot. (2015) Markov-switching generalized additive models. Statistics and Computing 27:1, pages 259-270.
Crossref
Nadja Klein & Thomas Kneib. (2016) Scale-Dependent Priors for Variance Parameters in Structured Additive Distributional Regression. Bayesian Analysis 11:4.
Crossref
Massimo Ventrucci, Daniela Cocchi & Marian Scott. (2016) Smoothing of land use maps for trend and change detection in urbanization. Environmental and Ecological Statistics 23:4, pages 565-584.
Crossref
Benjamin Hofner, Thomas Kneib & Torsten Hothorn. (2014) A unified framework of constrained regression. Statistics and Computing 26:1-2, pages 1-14.
Crossref
Théo Michelot, Roland Langrock, Thomas Kneib & Ruth King. (2016) Maximum penalized likelihood estimation in semiparametric mark-recapture-recovery models. Biometrical Journal 58:1, pages 222-239.
Crossref
Monica Gentili, Kim Isett, Nicoleta Serban & Julie Swann. (2015) Small-Area Estimation of Spatial Access to Care and Its Implications for Policy. Journal of Urban Health 92:5, pages 864-909.
Crossref
Thomas A. Murray, Brian P. Hobbs & Bradley P. Carlin. (2015) Combining nonexchangeable functional or survival data sources in oncology using generalized mixture commensurate priors. The Annals of Applied Statistics 9:3.
Crossref
Nadja Klein, Thomas Kneib, Stephan Klasen & Stefan Lang. (2015) Bayesian Structured Additive Distributional Regression for Multivariate Responses. Journal of the Royal Statistical Society Series C: Applied Statistics 64:4, pages 569-591.
Crossref
Roland Langrock, Thomas Kneib, Alexander Sohn & Stacy L. DeRuiter. (2015) Nonparametric inference in hidden Markov models using P-splines. Biometrics 71:2, pages 520-528.
Crossref
Yaeji Lim & Hee-Seok Oh. (2014) Simultaneous confidence interval for quantile regression. Computational Statistics 30:2, pages 345-358.
Crossref
Isabel Proença, Stefan Sperlich & Duygu Savaşcı. (2014) Semi-mixed effects gravity models for bilateral trade. Empirical Economics 48:1, pages 361-387.
Crossref
Brian P. HobbsChaan S. Ng. (2015) Inferring Stable Acquisition Durations for Applications of Perfusion Imaging in Oncology. Cancer Informatics 14s2, pages CIN.S17280.
Crossref
Lijie Gu & Lijian Yang. (2015) Oracally efficient estimation for single-index link function with simultaneous confidence band. Electronic Journal of Statistics 9:1.
Crossref
Mallory Nobles, Nicoleta Serban & Julie Swann. (2014) Spatial accessibility of pediatric primary healthcare: Measurement and inference. The Annals of Applied Statistics 8:4.
Crossref
Stefan Lang, Nikolaus Umlauf, Peter Wechselberger, Kenneth Harttgen & Thomas Kneib. (2012) Multilevel structured additive regression. Statistics and Computing 24:2, pages 223-238.
Crossref
Suigen Yang, Liugen Xue & Gaorong Li. (2014) Simultaneous confidence band for single-index random effects models with longitudinal data. Statistics & Probability Letters 85, pages 6-14.
Crossref
Hervé Cardot, David Degras & Etienne Josserand. (2013) Confidence bands for Horvitz–Thompson estimators using sampled noisy functional data. Bernoulli 19:5A.
Crossref
Zuofeng Shang & Guang Cheng. (2013) Local and global asymptotic inference in smoothing spline models. The Annals of Statistics 41:5.
Crossref
Roger Koenker. (2013) Discussion: Living beyond our means. Statistical Modelling 13:4, pages 323-333.
Crossref
Elisabeth Waldmann, Thomas Kneib, Yu Ryan Yue, Stefan Lang & Claudia Flexeder. (2013) Bayesian semiparametric additive quantile regression. Statistical Modelling 13:3, pages 223-252.
Crossref
Wolfgang Brunauer, Stefan Lang & Nikolaus Umlauf. (2013) Modelling house prices using multilevel structured additive regression. Statistical Modelling 13:2, pages 95-123.
Crossref
Martin P. Tingley & Peter Huybers. (2013) Recent temperature extremes at high northern latitudes unprecedented in the past 600 years. Nature 496:7444, pages 201-205.
Crossref
Iris Podolski, Elisa Belotti, Luděk Bufka, Holger Reulen & Marco Heurich. (2013) Seasonal and daily activity patterns of free‐living Eurasian lynx Lynx lynx in relation to availability of kills . Wildlife Biology 19:1, pages 69-77.
Crossref
Christoph Wunder, Andrea Wiencierz, Johannes Schwarze & Helmut Küchenhoff. (2013) Well-Being over the Life Span: Semiparametric Evidence from British and German Longitudinal Data. Review of Economics and Statistics 95:1, pages 154-167.
Crossref
Ludwig Fahrmeir, Thomas Kneib, Stefan Lang & Brian MarxLudwig Fahrmeir, Thomas Kneib, Stefan Lang & Brian Marx. 2013. Regression. Regression 413 533 .
K. De Brabanter, P. Karsmakers, J. De Brabanter, J.A.K. Suykens & B. De Moor. (2012) Confidence bands for least squares support vector machine classifiers: A regression approach. Pattern Recognition 45:6, pages 2280-2287.
Crossref
SIGRUNN H. SØRBYE & HÅVARD RUE. (2011) Simultaneous Credible Bands for Latent Gaussian Models. Scandinavian Journal of Statistics 38:4, pages 712-725.
Crossref
Peter PPtz & T. Kneib. (2016) A Penalized Spline Estimator for Fixed Effects Panel Data Models. SSRN Electronic Journal.
Crossref

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.