Testing for symmetric error distribution in nonparametric regression models
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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- Hyndman, R.J. & Yao, Q., 1998.
"Nonparametric Estimation and Symmetry Tests for Conditional Density Functions,"
Monash Econometrics and Business Statistics Working Papers
17/98, Monash University, Department of Econometrics and Business Statistics.
- Qiwei Yao & Rob J. Hyndman, 2002. "Nonparametric estimation and symmetry tests for conditional density functions," LSE Research Online Documents on Economics 6092, London School of Economics and Political Science, LSE Library.
- Koziol, James A., 1985. "A note on testing symmetry with estimated parameters," Statistics & Probability Letters, Elsevier, vol. 3(4), pages 227-230, July.
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