Translator Disclaimer
2011 Nonparametric conditional variance and error density estimation in regression models with dependent errors and predictors
Rafał Kulik, Cornelia Wichelhaus
Electron. J. Statist. 5: 856-898 (2011). DOI: 10.1214/11-EJS629

Abstract

This paper considers nonparametric regression models with long memory errors and predictors. Unlike in weak dependence situations, we show that the estimation of the conditional mean has influence on the estimation of both, the conditional variance and the error density. In particular, the estimation of the conditional mean has a negative effect on the asymptotic behaviour of the conditional variance estimator. On the other hand, surprisingly, estimation of the conditional mean may reduce convergence rates of the residual-based Parzen-Rosenblatt density estimator, as compared to the errors-based one. Our asymptotic results reveal small/large bandwidth dichotomous behaviour. In particular, we present a method which guarantees that a chosen bandwidth implies standard weakly dependent-type asymptotics. Our results are confirmed by an extensive simulation study. Furthermore, our theoretical lemmas may be used in different problems related to nonparametric regression with long memory, like cross-validation properties, bootstrap, goodness-of-fit or quadratic forms.

Citation

Download Citation

Rafał Kulik. Cornelia Wichelhaus. "Nonparametric conditional variance and error density estimation in regression models with dependent errors and predictors." Electron. J. Statist. 5 856 - 898, 2011. https://doi.org/10.1214/11-EJS629

Information

Published: 2011
First available in Project Euclid: 22 August 2011

zbMATH: 1274.62244
MathSciNet: MR2831519
Digital Object Identifier: 10.1214/11-EJS629

Subjects:
Primary: 62G05
Secondary: 62E20, 62G08, 62M10

Rights: Copyright © 2011 The Institute of Mathematical Statistics and the Bernoulli Society

JOURNAL ARTICLE
43 PAGES


SHARE
Back to Top