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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoArticle provided by Cambridge University Press in its journal Econometric Theory.
Volume (Year): 18 (2002)
Issue (Month): 05 (October)
Contact details of provider:
Postal: The Edinburgh Building, Shaftesbury Road, Cambridge CB2 2RU UK
Fax: +44 (0)1223 325150
Web page: http://journals.cambridge.org/jid_ECTProvider-Email:email@example.com
You can help add them by filling out this form.
CitEc Project, subscribe to its RSS feed for this item.
- 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.
- 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 Institute of Economics and Econometrics, Geneva School of Economics and Management, University of Geneva 12093, Institut d'Economie et Econométrie, Université de Genève.
- 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.
- 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.
- 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.
- Lavergne, Pascal & Patilea, Valentin, 2011.
"One for all and all for one: regression checks with many regressors,"
35779, University Library of Munich, Germany.
- 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.
- Pascal Lavergne & Valentin Patilea, 2007. "One for All and All for One : Regression Checks with Many Regressors”," Working Papers 2007-12, Centre de Recherche en Economie et Statistique.
- Emmanuel Guerre & Pascal Lavergne, 2004. "Data-Driven Rate-Optimal Specification Testing In Regression Models," Econometrics 0411008, EconWPA.
- 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.
- Richard Blundell & Joel L. Horowitz, 2007.
"A Non-Parametric Test of Exogeneity,"
Review of Economic Studies,
Oxford University Press, vol. 74(4), pages 1035-1058.
- 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.
- 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.
- Song, Kyungchul, 2010. "Testing semiparametric conditional moment restrictions using conditional martingale transforms," Journal of Econometrics, Elsevier, vol. 154(1), pages 74-84, January.
- 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.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Keith Waters).
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.