Robustness of the Restricted Maximum Likelihood Estimator Derived Under Normality as Applied to Data with Skewed Distributions

Abstract A one-way random model was used to simulate observations corresponding to sire and error variance components that were either skewed or normally distributed. The objectives were to investigate the dispersion and asymptotic biasedness properties of variance components estimated by an Expectation Maximization algorithm of the Restricted Maximum Likelihood estimator derived under normality when applied to these distributions. Results indicate that if the sire effects are distributed as a continuous normal variable, the dispersion of estimated sire variances is approximately normal regardless of the distribution of the error component. Similarly, the sire distribution had little effect on the estimated error variances when normal errors were generated. However, when either distribution was skewed, the variances of corresponding variance estimates increased. The skewed sire distributions increased the dispersion of heritability estimates. The mean variance estimates across replications indicate variance components estimated by Restricted Maximum Likelihood estimator are robust against skewness in terms of unbiasedness. Skewness may also be caused by the arbitrary scoring of a trait in subjective categories. To examine this, observations were classified in two through six classes coded as zero through five with respect to the number of classes. A separate analysis was performed with each set of classes. The greatest deviation of estimated variances from the true parameter occurred in the binomially distributed case. As the number of classes increased, the mean estimate asymptotically approached the true parameter. Estimates of heritability decreased as the occurrence of a score became rare within a class, regardless of the total number of classes.