Optimal Minimax Rates For Nonparametric Specification Testing In Regression Models
AbstractIn the context of testing the specification of a nonlinear parametric regression function, we adopt a nonparametric minimax approach to determine the maximum rate at which a set of smooth alternatives can approach the null hypothesis while ensuring that a test can uniformly detect any alternative in this set with some predetermined power. We show that a smooth nonparametric test has optimal asymptotic minimax properties for regular alternatives. As a by-product, we obtain the rate of the smoothing parameter that ensures rate-optimality of the test. We show that, in contrast, a class of nonsmooth tests, which includes the integrated conditional moment test of Bierens (1982, Journal of Econometrics 20, 105 134), has suboptimal asymptotic minimax properties.
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Bibliographic InfoArticle provided by Cambridge University Press in its journal Econometric Theory.
Volume (Year): 18 (2002)
Issue (Month): 05 (October)
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- Pascal Lavergne & Valentin Patilea, 2007.
"One for All and All for One : Regression Checks with Many Regressors”,"
2007-12, Centre de Recherche en Economie et Statistique.
- Pascal Lavergne & Valentin Patilea, 2008. "One for All and All for One:Regression Checks With Many Regressors," Discussion Papers dp08-06, Department of Economics, Simon Fraser University.
- Lavergne, Pascal & Patilea, Valentin, 2011. "One for all and all for one: regression checks with many regressors," MPRA Paper 35779, University Library of Munich, Germany.
- Juan M. Rodríguez-Póo & Stefan Sperlich & Philippe Vieu, 2012. "A Practical Test for Misspecification in Regression: Functional Form, Separability and Distribution," Research Papers by the Department of Economics, University of Geneva 12093, Département des Sciences Économiques, Université de Genève.
- Song, Kyungchul, 2010. "Testing semiparametric conditional moment restrictions using conditional martingale transforms," Journal of Econometrics, Elsevier, vol. 154(1), pages 74-84, January.
- Wenceslao González-Manteiga & Rosa Crujeiras, 2013. "An updated review of Goodness-of-Fit tests for regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 22(3), pages 361-411, September.
- Juan Carlos Escanciano & Kyungchul Song, 2007. "Asymptotically Optimal Tests for Single-Index Restrictions with a Focus on Average Partial Effects," PIER Working Paper Archive 07-005, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
- Joel Horowitz & Sokbae 'Simon' Lee, 2007.
"Testing a parametric quantile-regression model with an endogenous explanatory variable against a nonparametric alternative,"
CeMMAP working papers
CWP02/07, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
- Horowitz, Joel L. & Lee, Sokbae, 2009. "Testing a parametric quantile-regression model with an endogenous explanatory variable against a nonparametric alternative," Journal of Econometrics, Elsevier, vol. 152(2), pages 141-152, October.
- Richard Blundell & Joel Horowitz, 2004.
"A nonparametric test of exogeneity,"
CeMMAP working papers
CWP15/04, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
- Guay, Alain & Guerre, Emmanuel & Lazarová, Štěpána, 2013. "Robust adaptive rate-optimal testing for the white noise hypothesis," Journal of Econometrics, Elsevier, vol. 176(2), pages 134-145.
- Emmanuel Guerre & Pascal Lavergne, 2004. "Data-Driven Rate-Optimal Specification Testing In Regression Models," Econometrics 0411008, EconWPA.
- Felix Abramovich & Italia Feis & Theofanis Sapatinas, 2009. "Optimal testing for additivity in multiple nonparametric regression," Annals of the Institute of Statistical Mathematics, Springer, vol. 61(3), pages 691-714, September.
- Andrea Vaona, 2008. "The sensitivity of nonparametric misspecification tests to disturbance autocorrelation," Quaderni della facoltÃ di Scienze economiche dell'UniversitÃ di Lugano 0803, USI Università della Svizzera italiana.
- Pascal Lavergne & Valentin Patilea, 2006.
"Breaking the Curse of Dimensionality in Nonparametric Testing,"
2006-24, Centre de Recherche en Economie et Statistique.
- Lavergne, Pascal & Patilea, Valentin, 2008. "Breaking the curse of dimensionality in nonparametric testing," Journal of Econometrics, Elsevier, vol. 143(1), pages 103-122, March.
- Stefan Sperlich, 2013. "Comments on: An updated review of Goodness-of-Fit tests for regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 22(3), pages 419-427, September.
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