The Annals of Statistics

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

Alexander Korostelev

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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.

Article information

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

Dates
First available in Project Euclid: 20 September 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1032526957

Digital Object Identifier
doi:10.1214/aos/1032526957

Mathematical Reviews number (MathSciNet)
MR1401838

Zentralblatt MATH identifier
0862.62036

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

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

Citation

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. https://projecteuclid.org/euclid.aos/1032526957


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References

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  • DETROIT, MICHIGAN 48202 E-MAIL: apk@math.way ne.edu