Nonparametric Estimation via Convex Programming

Anatoli Juditsky (Anatoli.Juditskyimag.fr)
Arkadi Nemirovski (nemirovsisye.gatech.edu)

Abstract: In the paper, we focus primarily on the problem of recovering a linear form g'*x of unknown ``signal'' x known to belong to a given convex compact set X in R^n from N independent realizations of a random variable taking values in a finite set, the distribution p of the variable being affinely parameterized by x. With no additional assumptions on X and the dependence of p on x, we develop minimax optimal, within an absolute constant factor, and computationally efficient estimation routine. We then apply this routine to recovering x itself in the Euclidean norm.

Keywords: density estimation, inverse problems, convex optimization

Category 1: Applications -- Science and Engineering (Statistics )

Category 2: Convex and Nonsmooth Optimization (Convex Optimization )

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Entry Submitted: 08/23/2007
Entry Accepted: 08/23/2007
Entry Last Modified: 10/11/2007

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