Improved estimators of variance components with smaller probability of negativity

Abstract

A linear model with two variance components is considered, one variance component (say, σ 1 2 ≥0) corresponding to a random effect, and a second variance component (say, σ 2 >0) corresponding to the experimental errors. A class of invariant quadratic estimators (IQEs) is characterized, having uniformly smaller mean-squared error (MSE), and uniformly smaller probability of negativity, compared with the analysis-of-variance (ANOVA) estimator of σ 1 2