Nonparametric estimation of residual variance revisited

Abstract

Several difference-based estimators of residual variance are compared for finite sample size. Since the introduction of a rather simple estimator by Gasser, Sroka & Jennen-Steinmetz (1986) other proposals have been made. Here the one given by Hall, Kay & Titterington (1990) is of particular interest. It minimizes the asymptotic variance. Unfortunately it has severe problems with finite sample bias, and the estimator of Gasser et al. (1986) proves still to be a good choice. A new estimator is introduced, compromising between bias and variance.