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