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Goodness-of-fit tests for parametric regression models based on empirical characteristic functions. (English) Zbl 1186.62029
Summary: Test procedures are constructed for testing the goodness-of-fit in parametric regression models. The test statistic is in the form of an \(L^2\) distance between the empirical characteristic function of the residuals in a parametric regression fit and the corresponding empirical characteristic function of the residuals in a nonparametric regression fit. The asymptotic null distribution as well as the behavior of the test statistic under contiguous alternatives is investigated. Theoretical results are accompanied by a simulation study.

MSC:
62F05 Asymptotic properties of parametric tests
62J05 Linear regression; mixed models
62G10 Nonparametric hypothesis testing
65C60 Computational problems in statistics (MSC2010)
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