The Annals of Statistics

Asymptotics for kernel estimate of sliced inverse regression

Kai-Tai Fang and Li-Xing Zhu

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To explore nonlinear structures hidden in high-dimensional data and to estimate the effective dimension reduction directions in multivariate nonparametric regression, Li and Duan proposed the sliced inverse regression (SIR) method which is simple to use. In this paper, the asymptotic properties of the kernel estimate of sliced inverse regression are investigated. It turns out that regardless of the kernel function, the asymptotic distribution remains the same for a wide range of smoothing parameters.

Article information

Ann. Statist., Volume 24, Number 3 (1996), 1053-1068.

First available in Project Euclid: 20 September 2002

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Zentralblatt MATH identifier

Primary: 60F05: Central limit and other weak theorems 62G05: Estimation 62J02: General nonlinear regression

Data structure dimension reduction kernel estimation nonparametric regression sliced inverse regression


Zhu, Li-Xing; Fang, Kai-Tai. Asymptotics for kernel estimate of sliced inverse regression. Ann. Statist. 24 (1996), no. 3, 1053--1068. doi:10.1214/aos/1032526955.

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