Abstract
This paper addresses the problem of estimating means of Hudson (1978) type exponential families, where the vector of means lies in a closed convex set with a piecewise smooth boundary. Instead of Stein (1981)-like integration-by-parts technique, the Gauss divergence theorem is used to provide an inequality for evaluation of the risk function with respect to a quadratic loss. The inequality shows that a James and Stein (1961) type estimator is superior to the least squares estimator subject to restriction on the closed convex set.
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Tsukuma, H. Simultaneous estimation of restricted means via the gauss divergence theorem. Sankhya A 73, 110–124 (2011). https://doi.org/10.1007/s13171-011-0001-5
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DOI: https://doi.org/10.1007/s13171-011-0001-5