The Annals of Statistics

Nearest neighbor inverse regression

Tailen Hsing

Abstract

Sliced inverse regression (SIR), formally introduced by Li, is a very general procedure for performing dimension reduction in nonparametric regression. This paper considers a version of SIR in which the “slices” are determined by nearest neighbors and the response variable takes value possibly in a multidimensional space. It is shown, under general conditions, that the “effective dimension reduction space” can be estimated with rate $n^{-1/2}$ where $n$ is the sample size.

Article information

Source
Ann. Statist. Volume 27, Number 2 (1999), 697-731.

Dates
First available in Project Euclid: 5 April 2002

Permanent link to this document
http://projecteuclid.org/euclid.aos/1018031213

Digital Object Identifier
doi:10.1214/aos/1018031213

Mathematical Reviews number (MathSciNet)
MR1714711

Zentralblatt MATH identifier
0951.62034

Subjects
Primary: 62G05: Estimation
Secondary: 62F05: Asymptotic properties of tests

Citation

Hsing, Tailen. Nearest neighbor inverse regression. Ann. Statist. 27 (1999), no. 2, 697--731. doi:10.1214/aos/1018031213. http://projecteuclid.org/euclid.aos/1018031213.

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