Sankhya: The Indian Journal of Statistics

1999, Volume 61, Series B, Pt. 2, pp. 266-288

TO POOL OR NOT TO POOL: THE MULTIVARIATE DATA

By

S.E. AHMED and BASHIR ULLAH, University of Regina, Saskatchewan

SUMMARY. Two independent random samples are drawn from two multivariate normal populations with mean vectors m1 and m2, and the main interest is to estimate the mean vector m1 when it is a priori suspected that m1=m2. The uncertain prior information, in the form of m1=m2, is utilized in the estimation procedure. Improved pretest and the positive version of Stein-type estimator are proposed. It is shown analytically as well as computationally that the two proposed estimators dominate their standard forms. The percentage improvements of the proposed estimators over the usual estimator are calculated.

AMS (1991) subject classification. 62C10, 62H12, 62G05, 62G10.

Key words and phrases. Multivariate normal mean vector, uncertain prior information, pooling of means, quadratic biases and risks, improved pretest estimator, positive-part of Stein-type estimator.

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