The Annals of Statistics

Nearest neighbor inverse regression

Tailen Hsing

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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

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

First available in Project Euclid: 5 April 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Central limit theorem dimension reduction nonparametric regression sliced inverse regression.


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

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