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Tests for the error distribution in nonparametric possibly heteroscedastic regression models. (English) Zbl 1203.62069
Summary: Consistent procedures are constructed for testing the goodness-of-fit of the error distribution in nonparametric regression models. The test starts with a kernel-type regression fit and proceeds with the construction of a test statistic in the form of an $$L _{2}$$ distance between a parametric and a nonparametric estimates of the residual characteristic function. The asymptotic null distribution and the behavior of the test statistic under alternatives are investigated. A simulation study compares bootstrap versions of the proposed test to corresponding procedures utilizing the empirical distribution function.

##### MSC:
 62G08 Nonparametric regression and quantile regression 62E20 Asymptotic distribution theory in statistics 62G30 Order statistics; empirical distribution functions 62G10 Nonparametric hypothesis testing 62G20 Asymptotic properties of nonparametric inference 65C60 Computational problems in statistics (MSC2010)
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