TY - JOUR

T1 - Sufficient dimension reduction via inverse regression

T2 - A minimum discrepancy approach

AU - Cook, R. Dennis

AU - Ni, Liqiang

PY - 2005/6/1

Y1 - 2005/6/1

N2 - A family of dimension-reduction methods, the inverse regression (IR) family, is developed by minimizing a quadratic objective function. An optimal member of this family, the inverse regression estimator (IRE), is proposed, along with inference methods and a computational algorithm. The IRE has at least three desirable properties: (1) Its estimated basis of the central dimension reduction subspace is asymptotically efficient, (2) its test statistic for dimension has an asymptotic chi-squared distribution, and (3) it provides a chi-squared test of the conditional independence hypothesis that the response is independent of a selected subset of predictors given the remaining predictors. Current methods like sliced inverse regression belong to a suboptimal class of the IR family. Comparisons of these methods are reported through simulation studies. The approach developed here also allows a relatively straightforward derivation of the asymptotic null distribution of the test statistic for dimension used in sliced average variance estimation.

AB - A family of dimension-reduction methods, the inverse regression (IR) family, is developed by minimizing a quadratic objective function. An optimal member of this family, the inverse regression estimator (IRE), is proposed, along with inference methods and a computational algorithm. The IRE has at least three desirable properties: (1) Its estimated basis of the central dimension reduction subspace is asymptotically efficient, (2) its test statistic for dimension has an asymptotic chi-squared distribution, and (3) it provides a chi-squared test of the conditional independence hypothesis that the response is independent of a selected subset of predictors given the remaining predictors. Current methods like sliced inverse regression belong to a suboptimal class of the IR family. Comparisons of these methods are reported through simulation studies. The approach developed here also allows a relatively straightforward derivation of the asymptotic null distribution of the test statistic for dimension used in sliced average variance estimation.

KW - Inverse regression estimator

KW - Sliced average variance estimation

KW - Sliced inverse regression

KW - Sufficient dimension reduction

UR - http://www.scopus.com/inward/record.url?scp=20444454672&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=20444454672&partnerID=8YFLogxK

U2 - 10.1198/016214504000001501

DO - 10.1198/016214504000001501

M3 - Article

AN - SCOPUS:20444454672

VL - 100

SP - 410

EP - 428

JO - Journal of the American Statistical Association

JF - Journal of the American Statistical Association

SN - 0162-1459

IS - 470

ER -