Linear Approximate Bayes Estimator For Variance Components In Random Effects Model

Random effects model is widely applied in biology,engineering,sociology and other subject fields.The parameter estimator problem in random effects model is al-ways one of the most active research directions.The parameters studied in this paper are the variance components in the random effects model.For the variance components,some commonly used estimators are introduced in many literatures,such as uniformly minimum variance unbiased estimator,maximum likelihood estimator and Bayes esti-mator.The calculation of the Bayes estimator is usually very complicated,and even has no explicit form sometimes.In this paper,we employ a linear Bayes procedure to estimate the variance com-ponents in random effects model and propose a linear approximate Bayes estimator for the variance components,which has an analytical closed form and is easy to use.We obtain the expression of the linear approximate Bayes estimator.The superiorities of the proposed linear approximate Bayes estimator over the classical estimators and the linear approximate Bayes estimator based on several statistics are investigated in terms of the mean squared error matrix criterion.Numerical simulations show that the proposed linear approximate Bayes estimator is very close to the Bayes estimator,which is calculated via MCMC method,and the proposed linear approximate Bayes estimator even performs better than the Lindley’s approximation.We also compare the linear approximate Bayes estimator with Tier-ney and Kadane’s approximation by numerical simulations.In a real data application,we compute and compare the linear approximate Bayes estimator with the restricted maximum likelihood estimator.The numerical comparisons show that the linear ap-proximate Bayes estimator is reasonable and effective,which can be used to estimate the variance components in the random effects model.