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Biometrika 1971 58(1):230-233; doi:10.1093/biomet/58.1.230
© 1971 by Biometrika Trust
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MISCELLANEA

On the estimation of means in a bivariate normal distribution with equal marginal variances

M. AHSANULLAH {dagger}

Statistical Services Division, Food and Drug Directorate Ottawa

This paper considers the problem of estimation of the mean /1 of one of the components of a bivariate normal distribution with equal marginal variances from a sample of size n. The result of a preliminary test of hypothesis that the means /1 and /2 of the two components of the bivariate normal distribution are equal is used to define an estimator for /1. The bias and mean square error of this estimator are studied and the regions in the parameter space in which has smaller mean square error than the sample mean of the first component, are determined. The efficiency of this estimator relative to the usual estimator is tabulated and the tables can be used to determine a proper choice of significance level of the preliminary test.

Key Words: Estimation of means in bivariate normal populations • Mean square error and efficiency of point estimates. • Estimation after preliminary significance test • Bivariate normal populations with equal variances


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