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

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