Estimated confidence procedures for multivariate normal means
In estimation of a p-variate normal mean with identify covariance matrix, confidence sets recentered at Stein-type estimators have larger coverage probability then the usual confidence ellipsoids (see Hwang and Casella (1982)). However, the minimum coverage probability (say 1 - α) of these improved sets is identical to that of the usual sets, so that only 1 - α can be actually reported. Data dependent estimated confidence coefficients, 1 - Ĝa(X), can be found which (I) have frequentist validity, (II) are always larger than 1 - α, and (III) dominate the report of 1 - α via quadratic scoring. © 1989.
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