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- W2010449904 abstract "Abstract Consider the problem of estimating a p-variate normal mean using squared error loss. We demonstrate that contrary to what one might expect, (a) sup E{||d( X )||/|| X ||}>1 for p⩽2 , where the supremum is over all priors G symmetric about 0 , E(·) denotes marginal expectation corresponding to G and d( X ) denotes Bayes rule with respect to G. (b) The above supremum is equal to 1 for all p⩾3 . Thus Bayes estimates corresponding to symmetric priors can be expanders only in one and two dimensions. For p=1,2, the numerical values of the supremum are obtained. We also prove that sup E{||d( X )||/|| X ||}=1 for every p>1 if one restricts to spherically symmetric priors. In the process, some closed form formulas of independent interest are also obtained." @default.
- W2010449904 created "2016-06-24" @default.
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- W2010449904 date "2003-04-01" @default.
- W2010449904 modified "2023-10-18" @default.
- W2010449904 title "Bayes estimates as expanders in one and two dimensions" @default.
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- W2010449904 doi "https://doi.org/10.1016/s0378-3758(01)00301-9" @default.
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