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.
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Golubev, G.K. On a Method of Empirical Risk Minimization. Problems of Information Transmission 40, 202–211 (2004). https://doi.org/10.1023/B:PRIT.0000044256.20595.e6
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DOI: https://doi.org/10.1023/B:PRIT.0000044256.20595.e6