A minimaxity criterion in nonparametric regression based on large-deviations probabilities
The Annals of Statistics · 1996 · Volume 24 · Issue 3
Abstract
A large-deviations criterion is proposed for optimality of nonparametric regression estimators. The criterion is one of minimaxity of the large-deviations probabilities. We study the case where the underlying class of regression functions is either Lipschitz or Hölder, and when the loss function involves estimation at a point or in supremum norm. Exact minimax asymptotics are found in the Gaussian case.
Keywords
62G07; 62G20; exact asymptotics; Gaussian noise; large-deviations probabilities; minimax risk; Nonparametric regression;
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