The Annals of Statistics

Honest Confidence Regions for Nonparametric Regression

Ker-Chau Li

Full-text: Open access

Abstract

The problem of constructing honest confidence regions for nonparametric regression is considered. A lower rate of convergence, $n^{-1/4}$, for the size of the confidence region is established. The achievability of this rate is demonstrated using Stein's estimates and the associated unbiased risk estimates. Practical implications are discussed.

Article information

Source
Ann. Statist., Volume 17, Number 3 (1989), 1001-1008.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176347253

Digital Object Identifier
doi:10.1214/aos/1176347253

Mathematical Reviews number (MathSciNet)
MR1015135

Zentralblatt MATH identifier
0681.62047

JSTOR
links.jstor.org

Subjects
Primary: 62G99: None of the above, but in this section
Secondary: 62J99: None of the above, but in this section

Keywords
Adaptiveness confidence region convergence rate nonparametric regression Stein estimates Stein's unbiased risk estimates

Citation

Li, Ker-Chau. Honest Confidence Regions for Nonparametric Regression. Ann. Statist. 17 (1989), no. 3, 1001--1008. doi:10.1214/aos/1176347253. https://projecteuclid.org/euclid.aos/1176347253


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