Estimating Residual Variance in Nonparametric Regression Using Least Squares

• Activity Number: 486
• Type: Contributed
• Date/Time: Thursday, August 11, 2005 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Tiejun Tong*+ and Yuedong Wang
• Companies: University of California, Santa Barbara and University of California, Santa Barbara
• Keywords: Bandwidth ; Difference-based estimator ; Least square ; Nonparametric regression ; Quadratic forms ; Residual variance

Abstract

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 one dimensional domain with equally spaced design points, we show our method reaches an asymptotic optimal rate 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 easily to nonparametric regression models with multivariate functions defined on arbitrary subsets of normed spaces, possibly observed on unequally spaced or clustered design points.