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June, 1993 Adaptively Local One-Dimensional Subproblems with Application to a Deconvolution Problem
Jianqing Fan
Ann. Statist. 21(2): 600-610 (June, 1993). DOI: 10.1214/aos/1176349139

Abstract

In this paper, a method for finding global minimax lower bounds is introduced. The idea is to adjust automatically the direction of a local one-dimensional subproblem at each location to the nearly hardest one, and to use locally the difficulty of the one-dimensional subproblem. This method has the advantages of being easily implemented and understood. The lower bound is then applied to nonparametric deconvolution to obtain the optimal rates of convergence for estimating a whole function. Other applications are also addressed.

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Jianqing Fan. "Adaptively Local One-Dimensional Subproblems with Application to a Deconvolution Problem." Ann. Statist. 21 (2) 600 - 610, June, 1993. https://doi.org/10.1214/aos/1176349139

Information

Published: June, 1993
First available in Project Euclid: 12 April 2007

zbMATH: 0785.62038
MathSciNet: MR1232507
Digital Object Identifier: 10.1214/aos/1176349139

Subjects:
Primary: 62G07
Secondary: 62C20, 62G20

Rights: Copyright © 1993 Institute of Mathematical Statistics

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Vol.21 • No. 2 • June, 1993
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