Nearest neighbor inverse regression. (English) Zbl 0951.62034

Hsing, Tailen

Ann. Stat. 27, No. 2, 697-731 (1999).

Summary: Sliced inverse regression (SIR), formally introduced by K.-C. Li [J. Am. Stat. Assoc. 86, No. 414, 316-342 (1991; Zbl 0742.62044)], 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.

MSC:

62G08	Nonparametric regression and quantile regression
60F05	Central limit and other weak theorems
62G20	Asymptotic properties of nonparametric inference

Keywords:

central limit theorem; sliced inverse regression; dimension reduction

Citations:

Zbl 0742.62044

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