Sufficient dimension reduction based on an ensemble of minimum average variance estimators

Xiangrong Yin, Bing Li

Research output: Contribution to journalArticle

31 Citations (Scopus)

Abstract

We introduce a class of dimension reduction estimators based on an ensemble of the minimum average variance estimates of functions that characterize the central subspace, such as the characteristic functions, the Box-Cox transformations and wavelet basis. The ensemble estimators exhaustively estimate the central subspace without imposing restrictive conditions on the predictors, and have the same convergence rate as the minimum average variance estimates. They are flexible and easy to implement, and allow repeated use of the available sample, which enhances accuracy. They are applicable to both univariate and multivariate responses in a unified form.We establish the consistency and convergence rate of these estimators, and the consistency of a cross validation criterion for order determination. We compare the ensemble estimators with other estimators in a wide variety of models, and establish their competent performance.

Original languageEnglish (US)
Pages (from-to)3392-3416
Number of pages25
JournalAnnals of Statistics
Volume39
Issue number6
DOIs
StatePublished - Dec 2011

Fingerprint

Sufficient Dimension Reduction
Variance Estimator
Ensemble
Estimator
Central Subspace
Estimate
Multivariate Response
Box-Cox Transformation
Wavelet Bases
Dimension Reduction
Characteristic Function
Cross-validation
Univariate
Convergence Rate
Predictors
Rate of Convergence
Dimension reduction

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

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Sufficient dimension reduction based on an ensemble of minimum average variance estimators. / Yin, Xiangrong; Li, Bing.

In: Annals of Statistics, Vol. 39, No. 6, 12.2011, p. 3392-3416.

Research output: Contribution to journalArticle

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