Bernoulli

Asymptotically minimax estimation of a function with jumps

Catharina G.M. Oudshoorn

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Abstract

Asymptotically minimax nonparametric estimation of a regression function observed in white Gaussian noise over a bounded interval is considered, with respect to a L2-loss function. The unknown function f is assumed to be m times differentiable except for an unknown although finite number of jumps, with piecewise mth derivative bounded in L2 norm. An estimator is constructed, attaining the same optimal risk bound, known as Pinsker's constant, as in the case of smooth functions (without jumps).

Article information

Source
Bernoulli, Volume 4, Number 1 (1998), 15-33.

Dates
First available in Project Euclid: 6 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.bj/1175865488

Mathematical Reviews number (MathSciNet)
MR1611867

Zentralblatt MATH identifier
0920.62053

Keywords
jump-point estimation nonparametric regression optimal constant tapered orthogonal series estimator

Citation

Oudshoorn, Catharina G.M. Asymptotically minimax estimation of a function with jumps. Bernoulli 4 (1998), no. 1, 15--33. https://projecteuclid.org/euclid.bj/1175865488


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