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December 2009 Goodness-of-fit problem for errors in nonparametric regression: Distribution free approach
Estate V. Khmaladze, Hira L. Koul
Ann. Statist. 37(6A): 3165-3185 (December 2009). DOI: 10.1214/08-AOS680


This paper discusses asymptotically distribution free tests for the classical goodness-of-fit hypothesis of an error distribution in nonparametric regression models. These tests are based on the same martingale transform of the residual empirical process as used in the one sample location model. This transformation eliminates extra randomization due to covariates but not due the errors, which is intrinsically present in the estimators of the regression function. Thus, tests based on the transformed process have, generally, better power. The results of this paper are applicable as soon as asymptotic uniform linearity of nonparametric residual empirical process is available. In particular they are applicable under the conditions stipulated in recent papers of Akritas and Van Keilegom and Müller, Schick and Wefelmeyer.


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Estate V. Khmaladze. Hira L. Koul. "Goodness-of-fit problem for errors in nonparametric regression: Distribution free approach." Ann. Statist. 37 (6A) 3165 - 3185, December 2009.


Published: December 2009
First available in Project Euclid: 17 August 2009

zbMATH: 1369.62073
MathSciNet: MR2549556
Digital Object Identifier: 10.1214/08-AOS680

Primary: 62G08
Secondary: 62G10

Keywords: martingale transform , power

Rights: Copyright © 2009 Institute of Mathematical Statistics

Vol.37 • No. 6A • December 2009
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