  We consider the multiple testing of the general regression framework aiming
at studying the relationship between a univariate response and a p-dimensional
predictor. To test the hypothesis of the effect of each predictor, we construct
an Angular Balanced Statistic (ABS) based on the estimator of the sliced
inverse regression without assuming a model of the conditional distribution of
the response. According to the developed limiting distribution results in this
paper, we have shown that ABS is asymptotically symmetric with respect to zero
under the null hypothesis. We then propose a Model-free multiple Testing
procedure using Angular balanced statistics (MTA) and show theoretically that
the false discovery rate of this method is less than or equal to a designated
level asymptotically. Numerical evidence has shown that the MTA method is much
more powerful than its alternatives, subject to the control of the false
discovery rate.
