Minimax estimation of linear functionals over nonconvex parameter spaces

Minimax Estimation of Linear Functionals Over Nonconvex Parameter Spaces

The minimax theory for estimating linear functionals is extended to the case of a finite union of convex parameter spaces. Upper and lower bounds for the minimax risk can still be described in terms of a modulus of continuity. However in contrast to the theory for convex parameter spaces rate optimal procedures are often required to be nonlinear. A construction of such nonlinear procedures is g...

Minimax Estimation of Linear Functionals over Nonconvex Parameter Spaces1 by T. Tony Cai

The minimax theory for estimating linear functionals is extended to the case of a finite union of convex parameter spaces. Upper and lower bounds for the minimax risk can still be described in terms of a modulus of continuity. However in contrast to the theory for convex parameter spaces rate optimal procedures are often required to be nonlinear. A construction of such nonlinear procedures is g...

Reliable Minimax Parameter Estimation

This paper deals with the minimax parameter estimation of nonlinear parametric models from experimental data. Taking advantage of the special structure of the minimax problem, a new e¢cient and reliable algorithm based on interval constraint propagation is proposed. As an illustration, the ill-conditioned problem of estimating the parameters of a two-exponential model is considered.

Minimax Estimation of Quadratic Fourier Functionals

We study estimation of (semi-)inner products between two nonparametric probability distributions, given IID samples from each distribution. These products include relatively well-studied classical L and Sobolev inner products, as well as those induced by translation-invariant reproducing kernels, for which we believe our results are the first. We first propose estimators for these quantities, a...

Non linear estimation over weak Besov spaces and minimax Bayes method