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March 1998 Asymptotically minimax estimation of a function with jumps
Catharina G.M. Oudshoorn
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Bernoulli 4(1): 15-33 (March 1998).


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).


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Catharina G.M. Oudshoorn. "Asymptotically minimax estimation of a function with jumps." Bernoulli 4 (1) 15 - 33, March 1998.


Published: March 1998
First available in Project Euclid: 6 April 2007

zbMATH: 0920.62053
MathSciNet: MR1611867

Keywords: jump-point estimation , Nonparametric regression , optimal constant , tapered orthogonal series estimator

Rights: Copyright © 1998 Bernoulli Society for Mathematical Statistics and Probability

Vol.4 • No. 1 • March 1998
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