Year: 2009
Type: article
Abstract: 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.
Source: The Annals of Statistics
Authors: Estate V. Khmaladze, Hira L. Koul
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1984342243