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Omnibus tests for the error distribution in the linear regression model. (English) Zbl 1126.62059
Summary: A test procedure is constructed for testing goodness-of-fit of the error distribution in the regression context. The test statistic is based on an \(L^{2}\)-type distance between the characteristic function of the (assumed) error distribution and the empirical characteristic function of the residuals. The asymptotic null distribution as well as the behavior of the test statistic under contiguous alternatives is investigated, while the issue of the choice of suitable estimators has been particularly emphasized. Theoretical results are accompanied by a simulation study.

MSC:
62J05 Linear regression; mixed models
62F05 Asymptotic properties of parametric tests
62E20 Asymptotic distribution theory in statistics
60F05 Central limit and other weak theorems
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