The Annals of Statistics

A minimaxity criterion in nonparametric regression based on large-deviations probabilities

Alexander Korostelev

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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.

Article information

Ann. Statist., Volume 24, Number 3 (1996), 1075-1083.

First available in Project Euclid: 20 September 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G07: Density estimation 62G20: Asymptotic properties

Nonparametric regression Gaussian noise large-deviations probabilities minimax risk exact asymptotics


Korostelev, Alexander. A minimaxity criterion in nonparametric regression based on large-deviations probabilities. Ann. Statist. 24 (1996), no. 3, 1075--1083. doi:10.1214/aos/1032526957.

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