Document Type

Journal Article

Department/Unit

Department of Mathematics

Language

English

Abstract

Variance estimation is an important topic in nonparametric regression. In this paper, we propose a pairwise regression method for estimating the residual variance. Specifically, we regress the squared difference between observations on the squared distance between design points, and then estimate the residual variance as the intercept. Unlike most existing difference-based estimators that require a smooth regression function, our method applies to regression models with jump discontinuities. Our method also applies to the situations where the design points are unequally spaced. Finally, we conduct extensive simulation studies to evaluate the finite-sample performance of the proposed method and compare it with some existing competitors.

Keywords

difference-based estimator, jump point, non-uniform design, nonparametric regression, pairwise regression, residual variance

Publication Date

3-2014

Source Publication Title

Journal of Applied Statistics

Volume

41

Issue

3

Start Page

530

End Page

545

Publisher

Taylor & Francis

Peer Reviewed

1

Copyright

This is an Accepted Manuscript of an article published by Taylor & Francis in Journal of Applied Statistics in March 2014, available online: http://www.tandfonline.com/10.1080/02664763.2013.842962.

Funder

This researchwas supported by HongKongRGCgrantHKBU202711, and HongKong Baptist University grantsFRG2/10- 11/020 and FRG2/11-12/110. The authors thank the editor, the associate editor, and two referees for their helpful comments and suggestions that have substantially improved the paper.

DOI

10.1080/02664763.2013.842962

ISSN (print)

02664763

ISSN (electronic)

13600532

Included in

Mathematics Commons

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