作者：Liu, Molei; Katsevich, Eugene; Janson, Lucas; Ramdas, Aaditya
作者单位：Harvard University; Harvard T.H. Chan School of Public Health; University of Pennsylvania; Harvard University; Carnegie Mellon University
摘要：We consider the problem of conditional independence testing: given a response Y and covariates (X, Z), we test the null hypothesis that Y perpendicular to X | Z. The conditional randomization test was recently proposed as a way to use distributional information about X | Z to exactly and nonasymptotically control Type-I error using any test statistic in any dimensionality without assuming anything about Y | (X, Z). This flexibility, in principle, allows one to derive powerful test statistics f...
作者：Loper, J. H.; Lei, L.; Fithian, W.; Tansey, W.
作者单位：Columbia University; Stanford University; University of California System; University of California Berkeley; Memorial Sloan Kettering Cancer Center
摘要：We consider the problem of multiple hypothesis testing when there is a logical nested structure to the hypotheses. When one hypothesis is nested inside another, the outer hypothesis must be false if the inner hypothesis is false. We model the nested structure as a directed acyclic graph, including chain and tree graphs as special cases. Each node in the graph is a hypothesis and rejecting a node requires also rejecting all of its ancestors. We propose a general framework for adjusting node-lev...
