Bayes compound and empirical Bayes estimation of the mean of a Gaussian distribution on a Hilbert space
The paper studies the problem of finding admissible and asymptotically optimal compound and empirical Bayes rules when the component problem is estimation of the mean of a Gaussian distribution on a real, separable, infinite-dimensional Hilbert space under weighted squared-error-loss. The main result is that when the parameter space is a compact subset of the Hilbert space, a sequence of Bayes compound estimators versus a mixture of i.i.d. priors is asymptotically optimal if the mixing hyperprior has full support. The same result holds in the empirical Bayes formulation as well.
real, separable, infinite-dimensional Hilbert space
scientific article; zbMATH DE number 566958
scientific article