Principal Fitted Components for Dimension Reduction in Regression

被引：99

作者：

Cook, R. Dennis ^{[1
]}

Forzani, Liliana ^{[2
]}

机构：

[1] Univ Minnesota, Sch Stat, Minneapolis, MN 55455 USA

[2] Consejo Nacl Invest Cient & Tecn, Inst Matemat Aplicada Litoral, RA-3000 Buenos Aires, Santa Fe, Argentina

来源：

STATISTICAL SCIENCE | 2008年 / 23卷 / 04期

关键词：

Central subspace; dimension reduction; inverse regression; principal components;

D O I：

10.1214/08-STS275

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We provide a remedy for two concerns that have dogged the use of principal components in regression: (i) principal components are computed from the predictors alone and do not make apparent use of the response, and (ii) principal components are not invariant or equivariant under full rank linear transformation of the predictors. The development begins with principal fitted components [Cook, R. D. (2007). Fisher lecture: Dimension reduction in regression (with discussion). Statist. Sci. 22 1-26] and uses normal models for the inverse regression of the predictors on the response to gain reductive information for the forward regression of interest. This approach includes methodology for testing hypotheses about the number of components and about conditional independencies among the predictors.

引用

页码：485 / 501

页数：17

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