The Asymptotic Normality For The Simulation Method In Estimating The Variance Components For Repeated Measurements Model

Abstract

The simulation method is important to evaluate the properties of estimators, and through Asymptotic Normality for simulation we can approximate distributions of estimators and thus we can make important statistical inferences in making appropriate statistical decisions. In this research, a modification was made to the mean bias reduction method to estimate the variance components in the repeated measurements model by replacing the bias function in the mean bias reduction method with another that is dependent on a sample of independent observations that simulate the study model with variance components. As a result, we obtained a modified function converging with the mean bias reduction function, and from it, we find new estimators for the variance components of the repeated measurements model. This research aims to study the behavior of the new estimator of the variance components in the repeated measurements model resulting from the modified method on the mean bias reduction method by studying the asymptotic normality of the modified method estimator.