Romero-Padilla, J. M. 2016. Product moments of sample variances and correlation for variables with bivariate normal distribution. Journal of Mathematics and Statistics, 12 (1): 12-22. DOI: 10.3844/jmssp.2016.12.22
A preliminary test estimator of variance in the bivariate normal distribution is proposed after the Pitman–Morgan test of homogeneity of two variances. The bias and mean square error of the estimator 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.