Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

A least squares method for variance estimation in heteroscedastic nonparametric regression

Language

English

Abstract

Interest in variance estimation in nonparametric regression has grown greatly in the past several decades. Among the existing methods, the least squares estimator in Tong and Wang (2005) is shown to have nice statistical properties and is also easy to implement. Nevertheless, their method only applies to regression models with homoscedastic errors. In this paper, we propose two least squares estimators for the error variance in heteroscedastic nonparametric regression: the intercept estimator and the slope estimator. Both estimators are shown to be consistent and their asymptotic properties are investigated. Finally, we demonstrate through simulation studies that the proposed estimators perform better than the existing competitor in various settings. © 2014 Yuejin Zhou et al.

Publication Date

2014

Source Publication Title

Journal of Applied Mathematics

Volume

2014

Start Page

1

End Page

14

Publisher

Hindawi Publishing Corporation

DOI

10.1155/2014/585146

Link to Publisher's Edition

http://dx.doi.org/10.1155/2014/585146

ISSN (print)

1110757X

ISSN (electronic)

16870042

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