This article is cited in 2 papers

Methods of Signal Processing

On the Empirical Risk Minimization Method

G. K. Golubev<sup>ab

a</sup> Institute for Information Transmission Problems, Russian Academy of Sciences
^b Université de Provence

Abstract: We consider the problem of estimating an unknown vector observed in a simple white Gaussian noise model. For the estimation, a family of projection estimators is used; the problem is to choose, based on observations, the best estimator within this family. The paper studies a method for choosing a projection estimator, based on the principle of penalized empirical risk minimization. For this estimation method, nonasymptotic inequalities controlling its quadratic risk are given.

UDC: 621.391.1:519.2

Received: 24.12.2003
Revised: 31.05.2004

 English version: Problems of Information Transmission, 2004, 40:3, 202–211

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