Performance of Least Squares Lehmann-Scheffe Estimators of Variances Far Superior to those of Reml, ANOVA, Minque, and Ml

• Activity Number: 321
• Type: Contributed
• Date/Time: Wednesday, August 14, 2002 : 12:00 PM to 1:50 PM
• Sponsor: Biometrics Section*
• Author(s): William Slanger*+ and Janet Carlson
• Affiliation(s): North Dakota State University and North Dakota State University
• Keywords: Estimation ; Variance components ; Heritability

Abstract

Within confines of quadratic estimators and any linear model with any variance-covariance structure, Least Squares Lehmann-Scheffe estimators satisfy to maximum extent possible Lehmann-Scheffe criterion for uniformly best, unbiased estimation over the entire range of possible parameter values. For each of 96 combinations of six 3x4, n=39 unbalanced designs, eight combinations of error, interaction, and four-level main effect variance values, and two distributions (normal and chi-square-3df), 15000 vectors were generated. LSLS was compared to REML, ANOVA, MINQE, and ML via percentages of estimates within +/- 50% of parameter, mean square errors, variances, percentages of estimates that were positive, and biases. By all five measures, LSLS vastly outperformed the other four estimators in all 96 combinations. For example, averaged over four designs (nearly balanced and most unbalanced designs not included), average percentages the four methods for estimating the main effect variance, in order given above, performed relative to LSLS were -210, -200, -230, -94%; counts of number of times LSLS was better than other four methods or a method was better than LSLS were 603, 0, 15, 13, 9.