English

Empirical process of residuals for regression models with long memory errors

Statistics Theory 2011-02-23 v1 Statistics Theory

Abstract

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.

Keywords

Cite

@article{arxiv.1102.4368,
  title  = {Empirical process of residuals for regression models with long memory errors},
  author = {Pawel Lorek and Rafal Kulik},
  journal= {arXiv preprint arXiv:1102.4368},
  year   = {2011}
}
R2 v1 2026-06-21T17:29:40.821Z