Asymptotics for kernel estimate of sliced Inverse regression

LI-Xing Zhu, Kai-Tai Fang

Research output: Contribution to journalJournal articlepeer-review

174 Citations (Scopus)


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
Issue number3
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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