Testing for Symmetric Error Distribution in Nonparametric Regression Models

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Date

2003

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Publisher

Universitätsbibliothek Dortmund

Abstract

For the problem of testing symmetry of the error distribution in a nonparametric regression model we propose as a test statistic the difference between the two empirical distribution functions of estimated residuals and their counterparts with opposite signs. The weak convergence of the difference process to a Gaussian process is shown. The covariance structure of this process depends heavily on the density of the error distribution, and for this reason the performance of a symmetric wild bootstrap procedure is discussed in asymptotic theory and by means of a simulation study. In contrast to the available procedures the new test is also applicable under heteroscedasticity.

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Keywords

empirical process of residuals, testing for symmetry, nonparametric regression

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