Sankhya: The Indian Journal of Statistics

2003, Volume 65, Pt. 2, 411--421

Asymptotic Properties Of Stein-Type Confidence Sets --- A U-Statistics Approach

By

A.K. MD. EHSANES SALEH, Carleton University, Ottawa, Canada

SUMMARY: For a vector of estimable parameters Stein-type estimators are used to define recentered confidence sets. Asymptotically, we compare the coverage probabilities of these sets with constant volume using Pitman-type local alternatives. It is shown that the asymptotic coverage probability of the recentered confidence set based on the positive-    rule Stein estimator dominates the usual set. Also, the confidence set with preliminary test estimator as center is inadmissible.

AMS (1991) subject classification. 62F25, 62j07, 62C20.

Key words and phrases. Confidence sets, Stein estimation, asymptotic dominance.

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