Asymptotically Minimax Estimation of a Function with Jumps
Year: 1998
Type: article
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 2 -loss function. The unknown function f is assumed to be m times differentiable except for an unknown, though finite, number of jumps, with piecewise mth derivative bounded in L 2 -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). Key words: Jump-point estimation; Nonparametric regression; Optimal constant; Tapered orthogonal series estimator 1 Introduction In the eighties optimal rates of convergence in nonparametric regression estimation problems have been thoroughly examined, following the book of Ibragimov and Hasminskii (1981), the ground-breaking papers due to Stone (1982) and Birg'e (1983) and others. Later the interest has shifted to finding not only the optimal rates, but also the asymptotic optimal constants...
Source: Bernoulli
DOI: 10.2307/3318530
Author: Catharina G. M. Oudshoorn
Institution: University of Amsterdam
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2074459434