Asymptotics for kernel estimate of sliced Inverse regression

Lixing ZHU, Kai Tai Fang

Research output: Contribution to journalArticlepeer-review

146 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)1053-1068
Number of pages16
JournalAnnals of Statistics
Volume24
Issue number3
DOIs
Publication statusPublished - Jun 1996

Scopus Subject Areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

User-Defined Keywords

  • Data structure
  • Dimension reduction
  • Kernel estimation
  • Nonparametric regression
  • Sliced inverse regression

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