## The Annals of Statistics

### Honest Confidence Regions for Nonparametric Regression

Ker-Chau Li

#### 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

#### 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