Pinsker(1980) gave a precise asymptotic evaluation of the minimax mean squared error of estimation of a signal in Gaussian noise when the signal is known a priori to lie in a compact ellipsoid in Hilbert space. This `Minimax Bayes' method can be applied to a variety of global non-parametric estimation settings with parameter spaces far from ellipsoidal. For example it leads to a theory of exact...

In this paper, we study the minimax estimation of the Bochner integral μk(P ) := ∫

In this paper, we present some general results determining minimax bounds on statistical risk for density estimation based on certain information-theoretic considerations. These bounds depend only on metric entropy conditions and are used to identify the minimax rates of convergence.

The problem of the nonparametric minimax estimation of an innnitely smooth density at a given point, under random censorship, is considered. We establish the exact limiting behavior of the local minimax risk and propose the eecient kernel-type estimator based on the Kaplan-Meier estimator.

We study the Bayesian approach to nonparametric function estimation problems such as nonparametric regression and signal estimation. We consider the asymptotic properties of Bayes procedures for conjugate (=Gaussian) priors. We show that so long as the prior puts nonzero measure on the very large parameter set of interest then the Bayes estimators are not satisfactory. More specifically, we sho...

A 3 r m h estimating the parameter 0 from a parametrized signal problem (with 0 5 0 5 L) observed through Gaussian white noise, four useful and computable lower bounds for the Bayes risk were developed. For problems with different L and Merent signal to noise ratios, some bounds am superior to the others. The lower bound obtained from taking the maximum of the four, serves not only as a good lo...