On sliced inverse regression with high-dimensional covariates

Lixing ZHU*, Baiqi Miao, Heng PENG

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

152 Citations (Scopus)

Abstract

Sliced inverse regression is a promising method for the estimation of the central dimension-reduction subspace (CDR space) in semiparametric regression models. It is particularly useful in tackling cases with high-dimensional covariates. In this article we study the asymptotic behavior of the estimate of the CDR space with high-dimensional covariates, that is. when the dimension of the covariates goes to infinity as the sample size goes to infinity. Strong and weak convergence are obtained. We also suggest an estimation procedure of the Bayes information criterion type to ascertain the dimension of the CDR space and derive the consistency. A simulation study is conducted.

Original languageEnglish
Pages (from-to)630-643
Number of pages14
JournalJournal of the American Statistical Association
Volume101
Issue number474
DOIs
Publication statusPublished - Jun 2006

Scopus Subject Areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

User-Defined Keywords

  • Central dimension-reduction subspaee
  • Convergence rate
  • Dimensionality determination
  • Sliced inverse regression

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