Covariate Information Matrix for Sufficient Dimension Reduction

Weixin Yao, Debmalya Nandy, Bruce G. Lindsay, Francesca Chiaromonte

Research output: Contribution to journalArticle

Abstract

Building upon recent research on the applications of the density information matrix, we develop a tool for sufficient dimension reduction (SDR) in regression problems called covariate information matrix (CIM). CIM exhaustively identifies the central subspace (CS) and provides a rank ordering of the reduced covariates in terms of their regression information. Compared to other popular SDR methods, CIM does not require distributional assumptions on the covariates, or estimation of the mean regression function. CIM is implemented via eigen-decomposition of a matrix estimated with a previously developed efficient nonparametric density estimation technique. We also propose a bootstrap-based diagnostic plot for estimating the dimension of the CS. Results of simulations and real data applications demonstrate superior or competitive performance of CIM compared to that of some other SDR methods. Supplementary materials for this article are available online.

Original languageEnglish (US)
JournalJournal of the American Statistical Association
DOIs
StatePublished - Jan 1 2019

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Sufficient Dimension Reduction
Information Matrix
Covariates
Central Subspace
Reduction Method
Regression
Diagnostic Plot
Nonparametric Density Estimation
Regression Function
Density Matrix
Dimension reduction
Bootstrap
Decompose

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

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Covariate Information Matrix for Sufficient Dimension Reduction. / Yao, Weixin; Nandy, Debmalya; Lindsay, Bruce G.; Chiaromonte, Francesca.

In: Journal of the American Statistical Association, 01.01.2019.

Research output: Contribution to journalArticle

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