DOCUMENTA MATHEMATICA, Extra Volume ICM III (1998), 267-278

Iain M. Johnstone

Title: Oracle Inequalities and Nonparametric Function Estimation

In non-parametric function estimation, partial prior information about the unknown function is often expressed by a family of models or estimators, among which a choice must be made. Oracle inequalities bound the mean squared error of a given estimator in terms of the (unknowable) best possible choice of model for the unknown function. This survey concentrates on three examples: the James Stein estimator, soft thresholding, and complexity penalized least squares and as illustrations, we describe some consequences for adaptive estimation.

1991 Mathematics Subject Classification: 62G07, 62G20, 62C20

Keywords and Phrases: adaptive estimation, complexity penalty, James-Stein estimator, minimax estimation, thresholding, unconditional basis, wavelet shrinkage

Full text: dvi.gz 26 k, dvi 55 k, ps.gz 80 k.