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.

翻译：本文考虑一般回归框架下的多重检验问题，旨在研究单变量响应与p维预测变量之间的关系。为检验每个预测变量的效应，我们无需假设响应变量的条件分布模型，基于切片逆回归估计量构建了角度平衡统计量（ABS）。根据本文推导出的极限分布结果，我们证明了在零假设下ABS关于零点渐近对称。进而提出一种基于角度平衡统计量的无模型多重检验方法（MTA），并从理论上证明该方法的错误发现率渐近不超过预设水平。数值实验表明，在控制错误发现率的前提下，MTA方法的检验效力显著优于现有替代方法。