Relative Errors of Difference-Based Variance Estimators in Nonparametric Regression
Difference-based estimators for the error variance are popular since they do not require the estimation of the mean function. Unlike most existing difference-based estimators, new estimators proposed by Muller et al. (2003) and Tong and Wang (2005) achieved the asymptotic optimal rate as residual-based estimators. In this article, we study the relative errors of these difference-based estimators which lead to better understanding of the differences between them and residual-based estimators. To compute the relative error of the covariate-matched U-statistic estimator proposed by Muller et al. (2003), we develop a modified version by using simpler weights. We further investigate its asymptotic property for both equidistant and random designs and show that our modified estimator is asymptotically efficient.
Mean squared error;
Document Type: Research Article
Department of Applied Mathematics, University of Colorado, Boulder, Colorado, USA
Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts, USA
Department of Statistics and Applied Probability, University of California, Santa Barbara, California, USA
January 1, 2008