WIAS Preprint No. 281, (1996)

The Pinsker bound: a review


Authors

  • Nussbaum, Michael

2010 Mathematics Subject Classification

  • 62G07 62G20 62C20

Keywords

  • Signal estimation in Gaussian white noise, ellipsoid parameter spaces, asymptotic minimax risk, exact constants in nonparametric smoothing

DOI

10.20347/WIAS.PREPRINT.281

Abstract

We give an account of the Pinsker bound describing the exact asymptotics of the minimax risk in a class of nonparametric smoothing problems. The parameter spaces are Sobolev classes or ellipsoids, and the loss is of squared L2-type. The result from 1980 turned out to be a major step in the theory of nonparametric function estimation.

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