Efficiency loss and the linearity condition in dimension reduction

Yanyuan Ma, Liping Zhu

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

Linearity, sometimes jointly with constant variance, is routinely assumed in the context of sufficient dimension reduction. It is well understood that, when these conditions do not hold, blindly using them may lead to inconsistency in estimating the central subspace and the central mean subspace. Surprisingly, we discover that even if these conditions do hold, using them will bring efficiency loss. This paradoxical phenomenon is illustrated through sliced inverse regression and principal Hessian directions. The efficiency loss also applies to other dimension reduction procedures. We explain this empirical discovery by theoretical investigation.

Original languageEnglish (US)
Pages (from-to)371-383
Number of pages13
JournalBiometrika
Volume100
Issue number2
DOIs
StatePublished - Jun 1 2013

Fingerprint

Dimension Reduction
Linearity
Central Subspace
Sufficient Dimension Reduction
Sliced Inverse Regression
Inconsistency
Subspace
Dimension reduction
Direction compound
Context

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Mathematics(all)
  • Agricultural and Biological Sciences (miscellaneous)
  • Agricultural and Biological Sciences(all)
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

Cite this

Ma, Yanyuan ; Zhu, Liping. / Efficiency loss and the linearity condition in dimension reduction. In: Biometrika. 2013 ; Vol. 100, No. 2. pp. 371-383.
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Efficiency loss and the linearity condition in dimension reduction. / Ma, Yanyuan; Zhu, Liping.

In: Biometrika, Vol. 100, No. 2, 01.06.2013, p. 371-383.

Research output: Contribution to journalArticle

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