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Testing goodness of fit for the distribution of errors in multivariate linear models. (English) Zbl 1070.62029
Summary: To test goodness of fit to any fixed distribution of errors in multivariate linear models, we consider a weighted integral of the squared modulus of the difference between the empirical characteristic function of the residuals and the characteristic function under the null hypothesis. We study the limiting behaviour of this test statistic under the null hypothesis and under alternatives. In the asymptotics, the rank of the design matrix is allowed to grow with the sample size.

##### MSC:
 62G10 Nonparametric hypothesis testing 62J05 Linear regression; mixed models 62J20 Diagnostics, and linear inference and regression 62H15 Hypothesis testing in multivariate analysis 62E20 Asymptotic distribution theory in statistics
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