Some results on random design regression with long memory errors and predictors
Statistics Theory
2011-02-25 v1 Statistics Theory
Abstract
This paper studies nonparametric regression with long memory (LRD) errors and predictors. First, we formulate general conditions which guarantee the standard rate of convergence for a nonparametric kernel estimator. Second, we calculate the Mean Integrated Squared Error (MISE). In particular, we show that LRD of errors may influence MISE. On the other hand, an estimator for a shape function is typically not influenced by LRD in errors. Finally, we investigate properties of a data-driven bandwidth choice. We show that Averaged Squared Error (ASE) is a good approximation of MISE, however, this is not the case for a cross-validation criterion.
Cite
@article{arxiv.1102.4372,
title = {Some results on random design regression with long memory errors and predictors},
author = {Rafal Kulik and Pawel Lorek},
journal= {arXiv preprint arXiv:1102.4372},
year = {2011}
}