The Annals of Statistics

Adaptively Local One-Dimensional Subproblems with Application to a Deconvolution Problem

Jianqing Fan

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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.

Article information

Source
Ann. Statist., Volume 21, Number 2 (1993), 600-610.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176349139

Digital Object Identifier
doi:10.1214/aos/1176349139

Mathematical Reviews number (MathSciNet)
MR1232507

Zentralblatt MATH identifier
0785.62038

JSTOR
links.jstor.org

Subjects
Primary: 62G07: Density estimation
Secondary: 62C20: Minimax procedures 62G20: Asymptotic properties

Keywords
Cubical lower bound one-dimensional subproblems global rates of convergence minimax integrated risks deconvolution

Citation

Fan, Jianqing. Adaptively Local One-Dimensional Subproblems with Application to a Deconvolution Problem. Ann. Statist. 21 (1993), no. 2, 600--610. doi:10.1214/aos/1176349139. https://projecteuclid.org/euclid.aos/1176349139


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