Empirical process of residuals for regression models with long memory errors

Details Empirical process of residuals for regression models with long memory errors Empirical process of residuals for regression models with long memory errors

2011-02-21

arxiv.org/abs/1102.4368v1

Mathematics

Statistics Theory

Scientific paper

We consider the residual empirical process in random design regression with long memory errors. We establish its limiting behaviour, showing that its rates of convergence are different from the rates of convergence for to the empirical process based on (unobserved) errors. Also, we study a residual empirical process with estimated parameters. Its asymptotic distribution can be used to construct Kolmogorov-Smirnov, Cram\'{e}r-Smirnov-von Mises, or other goodness-of-fit tests. Theoretical results are justified by simulation studies.

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