Specification tests for the distribution of errors in nonparametric regression: a martingale approach

Juan Mora and Alicia Pérez-Alonso

Journal of Nonparametric Statistics, 2009, vol. 21, issue 4, 441-452

Abstract: We discuss how to test whether the distribution of regression errors belongs to a parametric family of continuous distribution functions, making no parametric assumption about the conditional mean or the conditional variance in the regression model. We propose using test statistics that are based on a martingale transform of the estimated empirical process. We prove that these statistics are asymptotically distribution-free, and two Monte Carlo experiments show that they work reasonably well in practice.

Date: 2009
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Working Paper: Specification Tests for the Distribution of Errors in Nonoarametric Regression: A Martingale Approach (2008)
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DOI: 10.1080/10485250802666192

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