Estimators of variance components in the augmented block design with new treatments from one or more populations

Abstract

This work compares by simulation estimates of variance components produced by the ANOVA (analysis of variance), ML (maximum likelihood), REML (restricted maximum likelihood), and MIVQUE(0) (minimum variance quadratic unbiased estimator) methods for augmented block design with additional treatments (progenies) stemming from one or more origins (crosses). Results showed the superiority of the MIVQUE(0) estimation. The ANOVA method, although unbiased, showed estimates with lower precision. The ML and REML methods produced downwards biased estimates for error variance (), and upwards biased estimates for genotypic variances (), particularly the ML method. Biases for the REML estimation became negligible when progenies were derived from a single cross, and experiments were of larger size with ratios / > 0.5. This method, however, provided the worst estimates for genotypic variances when progenies were derived from several crosses and the experiments were of small size (n < 120 observations).