Testing intersections of null-hypotheses is an integral part of closed testing procedures for assessing multiple null-hypotheses under family-wise type 1 error control. Popular intersection tests such as the minimum p-value test are based on marginal p-values and are typically evaluated conservatively by disregarding simultaneous behavior of the marginal p-values. We consider a general purpose Wald type test for testing intersections of one-sided null-hypotheses. The test is constructed on the basis of the simultaneous asymptotic behavior of the p values. The simultaneous asymptotic behavior is derived via influence functions of estimators using the so-called stacking approach. In particular, this approach does not require added assumptions on simultaneous behavior to be valid. The resulting test is shown to have attractive power properties and thus forms the basis of a powerful closed testing procedure for testing multiple one-sided hypotheses under family-wise type 1 error control.

翻译：检验零假设交集是控制族系第一类错误下评估多重零假设的闭合检验程序的重要组成部分。诸如最小p值检验等常用交集检验基于边际p值，通常通过忽略边际p值的联合行为进行保守评估。本文提出一种用于检验单边零假设交集的通用Wald型检验。该检验基于p值的联合渐近行为构建，其联合渐近行为通过采用所谓堆叠方法利用估计量的影响函数推导得出。特别地，该方法无需额外假设联合行为的有效性即可成立。研究证明所得检验具有优异的功效特性，从而为在控制族系第一类错误下检验多重单边假设提供了强效闭合检验程序的基础。