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January, 1976 Tail Minimaxity in Location Vector Problems and Its Applications
James O. Berger
Ann. Statist. 4(1): 33-50 (January, 1976). DOI: 10.1214/aos/1176343346


Let $X = (X_1,\cdots, X_p)^t, p \geqq 3$, have density $f(x - \theta)$ with respect to Lebesgue measure. It is desired to estimate $\theta = (\theta_1,\cdots, \theta_p)^t$ under the loss $L(\delta - \theta)$. Assuming the problem has a minimax risk $R_0$, an estimator is defined to be tail minimax if its risk is no larger than $R_0$ outside some compact set. Under quite general conditions on $f$ and $L$, sufficient conditions for an estimator to be tail minimax are given. A class of good tail minimax estimators is then developed and compared with the best invariant estimator.


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James O. Berger. "Tail Minimaxity in Location Vector Problems and Its Applications." Ann. Statist. 4 (1) 33 - 50, January, 1976.


Published: January, 1976
First available in Project Euclid: 12 April 2007

zbMATH: 0322.62008
MathSciNet: MR391319
Digital Object Identifier: 10.1214/aos/1176343346

Primary: 62C99
Secondary: 62F10 , 62H99

Keywords: best invariant estimator , location vector , minimax , risk function , tail minimax

Rights: Copyright © 1976 Institute of Mathematical Statistics


Vol.4 • No. 1 • January, 1976
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