## Journal of Applied Mathematics

### A Least Squares Method for Variance Estimation in Heteroscedastic Nonparametric Regression

#### 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.

#### Article information

Source
J. Appl. Math., Volume 2014 (2014), Article ID 585146, 14 pages.

Dates
First available in Project Euclid: 2 March 2015

https://projecteuclid.org/euclid.jam/1425305868

Digital Object Identifier
doi:10.1155/2014/585146

Mathematical Reviews number (MathSciNet)
MR3230576

#### Citation

Zhou, Yuejin; Cheng, Yebin; Tong, Tiejun. A Least Squares Method for Variance Estimation in Heteroscedastic Nonparametric Regression. J. Appl. Math. 2014 (2014), Article ID 585146, 14 pages. doi:10.1155/2014/585146. https://projecteuclid.org/euclid.jam/1425305868

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