论文标题
在切成逆回归中的多个假设的测试
On the testing of multiple hypothesis in sliced inverse regression
论文作者
论文摘要
我们考虑了旨在研究单变量响应与p维预测变量之间关系的一般回归框架的多重测试。为了测试每个预测因子效应的假设，我们基于切成薄片逆回归的估计量构建一个角平衡统计量（ABS），而无需假设响应的条件分布模型。根据本文开发的限制分布结果，我们表明ABS在零假设下相对于零是渐近的对称。然后，我们使用角平衡统计（MTA）提出了一个无模型的多重测试程序，从理论上讲，该方法的错误发现率小于或等于渐近指定的水平。数值证据表明，在控制错误发现率的情况下，MTA方法比其替代方案强大得多。
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.
