Estimating residual variance in nonparametric regression using least squares
成果类型：
Article
署名作者：
Tong, T; Wang, Y
署名单位：
University of California System; University of California Santa Barbara
刊物名称：
BIOMETRIKA
ISSN/ISSBN：
0006-3444
DOI：
10.1093/biomet/92.4.821
发表日期：
2005
页码：
821830
关键词：
摘要：
We propose a new estimator for the error variance in a nonparametric regression model. We estimate the error variance as the intercept in a simple linear regression model with squared differences of paired observations as the dependent variable and squared distances between the paired covariates as the regressor. For the special case of a one-dimensional domain with equally spaced design points, we show that our method reaches an asymptotic optimal rate which is not achieved by some existing methods. We conduct extensive simulations to evaluate finite-sample performance of our method and compare it with existing methods. Our method can be extended to nonparametric regression models with multivariate functions defined on arbitrary subsets of normed spaces, possibly observed on unequally spaced or clustered designed points.