B1893
Title: On the model-free testing of multiple hypothesis in sliced inverse regression
Authors: Zhigen Zhao - Temple University (United States) [presenting]
Xin Xing - Virginia Tech University (United States)
Abstract: The multiple testing of the general regression framework is considered, aiming at studying the relationship between a univariate response and a p-dimensional predictor. To test the hypothesis of the effect of each predictor, a mirror statistic is constructed 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, it is shown that the mirror statistic is asymptotically symmetric with respect to zero under the null hypothesis. The model-free multiple testing procedure is then proposed using Mirror statistics and it is shown 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 proposed method is much more powerful than its alternatives, subject to the control of the false discovery rate.
