Open Access
June 1996 Asymptotics for kernel estimate of sliced inverse regression
Li-Xing Zhu, Kai-Tai Fang
Ann. Statist. 24(3): 1053-1068 (June 1996). DOI: 10.1214/aos/1032526955


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.


Download Citation

Li-Xing Zhu. Kai-Tai Fang. "Asymptotics for kernel estimate of sliced inverse regression." Ann. Statist. 24 (3) 1053 - 1068, June 1996.


Published: June 1996
First available in Project Euclid: 20 September 2002

zbMATH: 0864.62027
MathSciNet: MR1401836
Digital Object Identifier: 10.1214/aos/1032526955

Primary: 60F05 , 62G05 , 62J02

Keywords: data structure , Dimension reduction , Kernel estimation , Nonparametric regression , sliced inverse regression

Rights: Copyright © 1996 Institute of Mathematical Statistics

Vol.24 • No. 3 • June 1996
Back to Top