Asymptotically Minimax Estimation of a Function with Jumps

Asymptotically Minimax Estimation of a Function with Jumps

Asymptotically minimax nonparametric estimation of a regression function observed in white Gaussian noise over a bounded interval is considered, with respect to a L 2-loss function. The unknown function f is assumed to be m times diierentiable except for an unknown, though nite, number of jumps, with piecewise mth derivative bounded in L 2-norm. An estimator is constructed, attaining the same o...

Asymptotically Minimax Non{parametric Function Estimation with Positivity Constraints I

Numerical Methods for Asymptotically Minimax Non{parametric Function Estimation with Positivity Constraints I

Asymptotically minimax Bayes predictive densities

fθ log (fθ/f̂) is used to examine various ways of choosing prior distributions; the principal type of choice studied is minimax. We seek asymptotically least favorable predictive densities for which the corresponding asymptotic risk is minimax. A result resembling Stein’s paradox for estimating normal means by the maximum likelihood holds for the uniform prior in the multivariate location family...

Asymptotically Minimax Robust Hypothesis Testing

The design of asymptotically minimax robust hypothesis testing is formalized for the Bayesian and Neyman-Pearson tests of Type I and II. The uncertainty classes based on the KL-divergence, αdivergence, symmetrized α-divergence, total variation distance, as well as the band model, moment classes and p-point classes are considered. It is shown with a counterexample that minimax robust tests do no...