A minimaxity criterion in nonparametric regression based on large-deviations probabilities. (English) Zbl 0862.62036

Summary: 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.


62G07 Density estimation
60F10 Large deviations
62G20 Asymptotic properties of nonparametric inference
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