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\noindent Statistica Sinica {\bf 17}(2007), 775-795

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\centerline{\large\bf TESTING FOR SYMMETRIC ERROR DISTRIBUTION IN}
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\centerline{\large\bf  NONPARAMETRIC REGRESSION MODELS}
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\author{Natalie Neumeyer and Holger Dette}
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\centerline{\it Universit\"at Hamburg and Ruhr-Universit\"at Bochum}

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\begin{quotation}
\noindent {\it Abstract:} For the problem of testing symmetry of the
error distribution in a nonparametric regression model, we
investigate the asymptotic properties of 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 available
procedures, the new test is  also applicable under
heteroscedasticity.\par \vspace{9pt} \noindent {\it Key words and
phrases:} Empirical process of residuals, testing for symmetry,
nonparametric regression. \par
\end{quotation}

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