Estimation Of Variance In Bivariate Normal Distribution After Preliminary Test Of Homogeneity
Abstract
A preliminary test estimator of variance in the bivariate normal distribution is proposed after Pitman-Morgan test of homogeneity of two variances. We propose one estimator of variance after preliminary test of two tails and another one for one tail test. The biases and mean square errors of both estimators are derived. The relative efficiency (RE) of the preliminary test estimator is studied. Computations and 3D graphs of RE for different parameters are analyzed. In order to get the maximum RE, recommendations of the significance level for the preliminary test are given for various sample sizes by using the max-min criterion.