  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.
