Dimension reduction in regressions through weighted variance estimation

Li Ping Zhu, Ya Ni Yang, Lixing ZHU*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Because sliced inverse regression (SIR) using the conditional mean of the inverse regression fails to recover the central subspace when the inverse regression mean degenerates, sliced average variance estimation (SAVE) using the conditional variance was proposed in the sufficient dimension reduction literature. However, the efficacy of SAVE depends heavily upon the number of slices. In the present article, we introduce a class of weighted variance estimation (WVE), which, similar to SAVE and simple contour regression (SCR), uses the conditional variance of the inverse regression to recover the central subspace. The strong consistency and the asymptotic normality of the kernel estimation of WVE are established under mild regularity conditions. Finite sample studies are carried out for comparison with existing methods and an application to a real data is presented for illustration.

Original languageEnglish
Pages (from-to)1929-1944
Number of pages16
JournalCommunications in Statistics - Theory and Methods
Volume40
Issue number11
DOIs
Publication statusPublished - Jan 2011

Scopus Subject Areas

  • Statistics and Probability

User-Defined Keywords

  • Asymptotic normality
  • Dimension reduction
  • Inverse regression
  • Simple contour regression
  • Sliced average variance estimation

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