Abstract
Assume $X = (X_1,\cdots, X_p)^t$ has a $p$-variate density, with respect to Lebesgue measure, of the form $f((x - \theta)^t\not\sum^{-1}(x - \theta))$. Here $\not\sum$ is a known positive definite $p \times p$ matrix and $p \geqq 3$. Assume either (i) $f$ is completely monotonic, or (ii) there exist $\alpha > 0$ and $K > 0$ for which $h(s) = f(s)e^{\alpha s}$ is nondecreasing and nonzero if $s > K$. Then for estimating $\theta$ under a known quadratic loss, classes of minimax estimators are found.
Citation
James Berger. "Minimax Estimation of Location Vectors for a Wide Class of Densities." Ann. Statist. 3 (6) 1318 - 1328, November, 1975. https://doi.org/10.1214/aos/1176343287
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