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Bootstrap tests for the error distribution in linear and nonparametric regression models. (English) Zbl 1108.62032
Summary: We investigate several tests for the hypothesis of a parametric form of the error distribution in the common linear and nonparametric regression model, which are based on empirical processes of residuals. It is well known that tests in this context are not asymptotically distribution-free and the parametric bootstrap is applied to deal with this problem.
The performance of the resulting bootstrap test is investigated from an asymptotic point of view and by means of a simulation study. The results demonstrate that even for moderate sample sizes the parametric bootstrap provides a reliable and easy accessible solution to the problem of goodness-of-fit testing of assumptions regarding the error distribution in linear and nonparametric regression models.

MSC:
62F40 Bootstrap, jackknife and other resampling methods
62G08 Nonparametric regression and quantile regression
62J05 Linear regression; mixed models
62F05 Asymptotic properties of parametric tests
62F03 Parametric hypothesis testing
62G10 Nonparametric hypothesis testing
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