Abstract

Aggregating estimators using exponential weights depending on their risk performs well in expectation, but sadly not in probability. Considering exponential weights of a penalized risk is a way to overcome this issue. We focus on the fixed design regression framework with sub-Gaussian noise and provide penalties allowing to obtain oracle inequalities in deviation for the aggregation of affine estimators. Sharp oracle inequalities are provided by a condition using the regression function's norm. MSC 2010 subject classifications: Primary 62G08; secondary 62J02.

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