## The Annals of Statistics

### Testing predictor contributions in sufficient dimension reduction

R. Dennis Cook

#### 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.

#### Article information

Source
Ann. Statist. Volume 32, Number 3 (2004), 1062-1092.

Dates
First available in Project Euclid: 24 May 2004

http://projecteuclid.org/euclid.aos/1085408495

Digital Object Identifier
doi:10.1214/009053604000000292

Mathematical Reviews number (MathSciNet)
MR2065198

Zentralblatt MATH identifier
02100793

Subjects
Primary: 62G08: Nonparametric regression
Secondary: 62G09: Resampling methods 62H05: Characterization and structure theory

#### Citation

Cook, R. Dennis. Testing predictor contributions in sufficient dimension reduction. Ann. Statist. 32 (2004), no. 3, 1062--1092. doi:10.1214/009053604000000292. http://projecteuclid.org/euclid.aos/1085408495.

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