Testing predictor contributions in sufficient dimension reduction

2004/05/27 by R. Dennis Cook · 3 citations
Mathematics · #Advanced Statistical Methods and Models #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #math.ST #msc:62G08 #msc:62G09 #msc:62H05. #stat.TH

paper · pdf · doi:10.1214/009053604000000292

published as Annals of Statistics 2004, Vol. 32, No. 3, 1062-1092

openalex publication_date 2004/05/27 · arxiv created 2004/06/25 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We develop tests of the hypothesis of no effect for selected predictors in regression, without assuming a model for the conditional distribution of the response given the predictors. Predictor effects need not be limited to the mean function and smoothing is not required. The general approach is based on sufficient dimension reduction, the idea being to replace the predictor vector with a lower-dimensional version without loss of information on the regression. Methodology using sliced inverse regression is developed in detail.

Cited by

• Dimension reduction based on constrained canonical correlation and variable filtering
• Estimating sufficient reductions of the predictors in abundant high-dimensional regressions
• A Model-free Variable Screening Method Based on Leverage Score