Minimax bounds for estimation of normal mixtures

Minimax lower bounds for estimation

Ensemble Minimax Estimation for Multivariate Normal Means

This article discusses estimation of a heteroscedastic multivariate normal mean in terms of the ensemble risk. We first derive the ensemble minimaxity properties of various estimators that shrink towards zero. We then generalize our results to the case where the variances are given as a common unknown but estimable chi-squared random variable scaled by different known factors. We further provid...

Local Privacy and Minimax Bounds: Sharp Rates for Probability Estimation

We provide a detailed study of the estimation of probability distributions— discrete and continuous—in a stringent setting in which data is kept private even from the statistician. We give sharp minimax rates of convergence for estimation in these locally private settings, exhibiting fundamental trade-offs between privacy and convergence rate, as well as providing tools to allow movement along ...

Minimax lower bounds for function estimation on graphs

In recent years there has been substantial interest in high-dimensional estimation and prediction problems on large graphs. These can in many cases be seen as high-dimensional or nonparametric regression or classification problems in which the goal is to learn a “smooth” function on a given graph. Various methods have been proposed to deal with such problems, motivated by a variety of applicati...

Minimax Bounds for Autoregressive Approximations

The subject of this paper is autoregressive AR approximations of a stationary Gaus sian discrete time process based on a nite sequence of observations We adopt the non parametric minimax framework and study how well can the process be approximated by a nite order autoregressive model Our results show that a properly chosen model dimen sion leads to an optimal in order minimax estimator