Estimating one mean of a bivariate normal distribution using a preliminary test of significance and a two-stage sampling scheme
Title:
Estimating one mean of a bivariate normal distribution using a preliminary test of significance and a two-stage sampling scheme
Author:
Brogan, Donna R. Sedransk, Joseph
Appeared in:
Communications in statistics
Paging:
Volume 7 (1978) nr. 2 pages 173-186
Year:
1978
Contents:
Let (X,Y) have a bivariate normal distribution with unknown mean vector (y ,y K and known covariamce matrix E. It is desired A i to estimate y . A first stage sample is obtained on (X,Y), X only, and Y only, A preliminary test of Hn: y = y is performed, the U I A result of which specifies a second-stage sample. The estimator of y is either a regression estimator or a pooled estimator which pools estimators of y and y v The bias and mean square error (MSE) of this estimation procedure are derived, and a numerical example is discussed, It appears that the effects on the estimatorfs bias and MSE of (1) the level of significance of the test of Hn, and (2) a standardized measure of the difference between yy and y , are similar to those reported by investigators of related problems, Moreover, an increase in PW1 will generally decrease the MSE
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