A Comparison of Variance Component Estimates for Arbitrary Underlying Distributions

Abstract

Abstract Large-sample covariance matrices for the analysis of variance (ANOVA), minimum norm quadratic unbiased estimator (MINQUE), restricted maximum likelihood (REML), and maximum likelihood (ML) estimates of variance components are presented for the unbalanced one-way model when the underlying distributions are not necessarily normal. The limiting variances depend on the design sequence, on the actual values of the variance components, and on the kurtosis parameters of the underlying distributions. (The skewness parameters and other moments do not affect the limiting distributions.) Because all estimates are consistent and asymptotically normal, it is reasonable to compare the estimates using their asymptotic variances. Thus the efficiency of one estimate relative to another is defined as the ratio of their asymptotic variances, and these efficiencies are evaluated numerically and analytically for a variety of nonnormal situations. Various authors, including Hocking and Kutner (1975), Corbeil and Searl...