Covariate Information Matrix for Sufficient Dimension Reduction

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

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

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)
Pages (from-to)1752-1764
Number of pages13
JournalJournal of the American Statistical Association
Volume114
Issue number528
DOIs
StatePublished - Oct 2 2019

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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