Some Results on Biased Linear Estimation Applied to Variance Component Estimation

Abstract

Shortcomings of commonly used estimators of variance components have been noted often in previous work. Hodges and Lehmann [2] noted that the sample variance is dominated by a simple multiple of itself. Klotz, Milton and Zacks [3] demonstrated that the customarily-used estimator of the among-groups variance component in the balanced, random, one-way analysis of variance (ANOVA) ‘model may be dominated by various estimators. Harville [1] established similar results for the two-way mixed ANOVA model. Olsen, Seely and Birkes [6] established conditions for admissibility in the class of unbiased invariant quadratic estimators in models with two variance components and noted that some standard estimators are not admissible in this class (see also Seely [7]). LaMotte [4] identified biased invariant quadratic estimators which dominate the ANOVA estimator of the among groups variance component in the unbalanced one-way random ANOVA model.KeywordsVariance ComponentNormal Random VariableLinear EstimatorMixed ANOVA ModelClosed Convex ConeThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.