On efficient dimension reduction with respect to a statistical functional of interest

Wei Luo, Bing Li, Xiangrong Yin

Research output: Contribution to journalArticle

11 Scopus citations

Abstract

We introduce a new sufficient dimension reduction framework that targets a statistical functional of interest, and propose an efficient estimator for the semiparametric estimation problems of this type. The statistical functional covers a wide range of applications, such as conditional mean, conditional variance and conditional quantile. We derive the general forms of the efficient score and efficient information as well as their specific forms for three important statistical functionals: the linear functional, the composite linear functional and the implicit functional. In conjunction with our theoretical analysis, we also propose a class of one-step Newton-Raphson estimators and show by simulations that they substantially outperform existing methods. Finally, we apply the new method to construct the central mean and central variance subspaces for a data set involving the physical measurements and age of abalones, which exhibits a strong pattern of heteroscedasticity.

Original languageEnglish (US)
Pages (from-to)382-412
Number of pages31
JournalAnnals of Statistics
Volume42
Issue number1
DOIs
StatePublished - Jan 1 2014

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All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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