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