Asymptotically minimax estimation of a function with jumps

Research output: Contribution to journalArticleAcademicpeer-review

11 Downloads (Pure)

Abstract

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
JournalBernoulli
Volume4
Issue number1
Publication statusPublished - Mar 1998
Externally publishedYes

Keywords

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

Cite this