Estimating the error variance in nonparametric regression by a covariate-matched u-statistic

Ursula U. Müller, Anton Schick, Wolfgang Wefelmeyer
2003 Statistics (Berlin)  
For nonparametric regression models with fixed and random design, two classes of estimators for the error variance have been introduced: second sample moments based on residuals from a nonparametric fit, and difference-based estimators. The former are asymptotically optimal but require estimating the regression function; the latter are simple but have larger asymptotic variance. For nonparametric regression models with random covariates, we introduce a class of estimators for the error variance
more » ... that are related to difference-based estimators: covariate-matched U-statistics. We give conditions on the random weights involved that lead to asymptotically optimal estimators of the error variance. Our explicit construction of the weights uses a kernel estimator for the covariate density.
doi:10.1080/0233188031000078051 fatcat:dglomhvpmval7ekr7km7mb4cpq