Department of Mathematics
A least squares method for variance estimation in heteroscedastic nonparametric regression
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.
Source Publication Title
Journal of Applied Mathematics
Hindawi Publishing Corporation
Zhou, Yuejin, Yebin Cheng, and Tiejun Tong. "A least squares method for variance estimation in heteroscedastic nonparametric regression." Journal of Applied Mathematics 2014 (2014): 1-14.