Dimension reduction for nonelliptically distributed predictors

Bing Li, Yuexiao Dong

Research output: Contribution to journalArticle

73 Scopus citations

Abstract

Sufficient dimension reduction methods often require stringent conditions on the joint distribution of the predictor, or, when such conditions are not satisfied, rely on marginal transformation or reweighting to fulfill them approximately. For example, a typical dimension reduction method would require the predictor to have elliptical or even multivariate normal distribution. In this paper, we reformulate the commonly used dimension reduction methods, via the notion of "central solution space," so as to circumvent the requirements of such strong assumptions, while at the same time preserve the desirable properties of the classical methods, such as √ n-consistency and asymptotic normality. Imposing elliptical distributions or even stronger assumptions on predictors is often considered as the necessary tradeoff for overcoming the "curse of dimensionality," but the development of this paper shows that this need not be the case. The new methods will be compared with existing methods by simulation and applied to a data set.

Original languageEnglish (US)
Pages (from-to)1272-1298
Number of pages27
JournalAnnals of Statistics
Volume37
Issue number3
DOIs
StatePublished - Jun 1 2009

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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