Dimension reduction in regressions through cumulative slicing estimation

Li Ping Zhu*, Lixing ZHU, Zheng Hui Feng

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

86 Citations (Scopus)

Abstract

In this paper we offer a complete methodology of cumulative slicing estimation to sufficient dimension reduction. In parallel to the classical slicing estimation, we develop three methods that are termed, respectively, as cumulative mean estimation, cumulative variance estimation, and cumulative directional regression. The strong consistency for p = O(n1/2/log n) and the asymptotic normality for p = o(n1/2) are established, where p is the dimension of the predictors and n is sample size. Such asymptotic results improve the rate p = o(n1/3) in many existing contexts of semiparametric modeling. In addition, we propose a modified BIC-type criterion to estimate the structural dimension of the central subspace. Its consistency is established when p = o(n1/2). Extensive simulations are carried out for comparison with existing methods and a real data example is presented for illustration.

Original languageEnglish
Pages (from-to)1455-1466
Number of pages12
JournalJournal of the American Statistical Association
Volume105
Issue number492
DOIs
Publication statusPublished - Dec 2010

Scopus Subject Areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

User-Defined Keywords

  • Inverse regression
  • Slicing estimation
  • Sufficient dimension reduction
  • Ultrahigh dimensionality

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