Asymptotically minimax estimation of a function with jumps

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Asymptotically minimax nonparametric estimation of a regression function observed in white Gaussian noise over a bounded interval is considered, with respect to a L<sub>2</sub>-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 L<sub>2</sub> 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).
Original languageEnglish
Pages (from-to)15-33
Number of pages19
Issue number1
Publication statusPublished - Mar 1998
Externally publishedYes


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

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