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.
"Testing predictor contributions in sufficient dimension reduction." Ann. Statist. 32 (3) 1062 - 1092, June 2004. https://doi.org/10.1214/009053604000000292