Department of Mathematics
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.
Source Publication Title
Journal of Applied Mathematics
Hindawi Publishing Corporation
2014 Yuejin Zhou et al. This is an open access article distributed under the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited
Yebin Cheng’s research was supported in part by National Natural Science Foundation of China Grant no. 11271241 and Shanghai Leading Academic Discipline Project no. 863. Tiejun Tong’s research was supported in part by Hong Kong Research Grant HKBU202711 and Hong Kong Baptist University FRG Grants FRG2/10-11/020 and FRG2/11-12/110. Yuejin Zhou’s research was supported in part by Doctoral Innovation Foundation of SHUFE CXJJ-2011-442.
Link to Publisher's Edition
Zhou, Y., Cheng, Y., & Tong, T. (2014). A least squares method for variance estimation in heteroscedastic nonparametric regression. Journal of Applied Mathematics, 2014, 1-14. https://doi.org/10.1155/2014/585146