Abstract
ABSTRACT There are many versions of Bayesian Cramér-Rao type lower bounds of the Bayes risk. We compare them from the point of view of asymptotic optimality. We show that the asymptotic optimality result still holds true in the sense of Bhattacharyya type lower bound in univariate case. And we show the asymptotic optimal choice in the Gill-Levit bound in multivariate case. As an application of it, we also show a lower bound for the Bayesian risk with a nuisance parameter.
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