We consider the estimation of the mean Ö of a £i-exponential multivariate distribution with density i ^ j^exp (-J!^), where ||i,||, = ZLi lf 0 is a scale parameter. We investigate the general class of estimators, X + g{X), and show they dominate the minimum risk equivariant estimator X under the usual quadratic loss ||i5(A') -where llfll = (EiLi I/.-)'^^ is the Eudidean norm in K'. When er = 1, the main domination condition is obtained through the partial differential inequality 4 divff + 2X • S^g + ||s|p < 0. We also consider the case where u is unknown. Furthermore we also treat the general case where the sampling distribution is a Scale mixture of £i-exponential distributions.
The estimation of the location parameter of an a 1 -symmetric distribution is considered. Specifically when a p-dimensional random vector has a distribution that is a mixture of uniform distributions on the a 1 -sphere, we investigate a general class of estimators of the form d=X+g. Under the usual quadratic loss, domination of d over X is obtained through the partial differential inequality 4 div g+2X · "
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