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Testing predictor contributions in sufficient dimension reduction. (English) Zbl 1092.62046
Summary: 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.

MSC:
62G08 Nonparametric regression and quantile regression
62H05 Characterization and structure theory for multivariate probability distributions; copulas
62E20 Asymptotic distribution theory in statistics
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