Partial inverse regression

Lexin Li, R. Dennis Cook, Chih Ling Tsai

Research output: Contribution to journalArticlepeer-review

31 Scopus citations

Abstract

In regression with a vector of quantitative predictors, sufficient dimension reduction methods can effectively reduce the predictor dimension, while preserving full regression information and assuming no parametric model. However, all current reduction methods require the sample size n to be greater than the number of predictors p. It is well known that partial least squares can deal with problems with np. We first establish a link between partial least squares and sufficient dimension reduction. Motivated by this link, we then propose a new dimension reduction method, entitled partial inverse regression. We show that its sample estimator is consistent, and that its performance is similar to or superior to partial least squares when np, especially when the regression model is nonlinear or heteroscedastic. An example involving the spectroscopy analysis of biscuit dough is also given.

Original languageEnglish (US)
Pages (from-to)615-625
Number of pages11
JournalBiometrika
Volume94
Issue number3
DOIs
StatePublished - Sep 14 2007

Keywords

  • Partial least squares
  • Single-index model
  • Sliced inverse regression

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