Guilbaud Olivier
Sköndalsbrovägen, Sköndal, Sweden.
Biom J. 2012 May;54(3):317-42. doi: 10.1002/bimj.201100123.
The derivation of simultaneous confidence regions for some multiple-testing procedures (MTPs) of practical interest has remained an unsolved problem. This is the case, for example, for Hochberg's step-up MTP and Hommel's more powerful MTP that is neither a step-up nor a step-down procedure. It is shown in this article how the direct approach used previously by the author to construct confidence regions for certain closed-testing procedures (CTPs) can be extended to a rather general setup. The general results are then applied to a situation with one-sided inferences and CTPs belonging to a class studied by Wei Liu. This class consists of CTPs based on ordered marginal p-values. It includes Holm's, Hochberg's, and Hommel's MTPs. A property of the confidence regions derived for these three MTPs is that no confidence assertions sharper than rejection assertions can be made unless all null hypotheses are rejected. Briefly, this is related to the fact that these MTPs are quite powerful. The class of CTPs considered includes, however, also MTPs related to Holm's, Hochberg's, and Hommel's MTPs that are less powerful but are such that confidence assertions sharper than rejection assertions are possible even if not all null hypotheses are rejected. One may thus choose and prespecify such an MTP, though this is at the cost of less rejection power.
对于一些具有实际意义的多重检验程序（MTP），同时置信区域的推导仍然是一个未解决的问题。例如，霍赫伯格的逐步MTP以及霍梅尔更强大的MTP（它既不是逐步程序也不是逐步递减程序）就是这种情况。本文展示了作者先前用于为某些封闭检验程序（CTP）构建置信区域的直接方法如何能够扩展到一个相当一般的设定。然后将这些一般结果应用于单边推断以及属于刘薇所研究的一类CTP的情况。这类CTP由基于有序边际p值的CTP组成。它包括霍尔姆的、霍赫伯格的和霍梅尔的MTP。为这三种MTP推导的置信区域的一个性质是，除非所有原假设都被拒绝，否则不能做出比拒绝断言更精确的置信断言。简而言之，这与这些MTP相当强大这一事实有关。然而，所考虑的CTP类还包括与霍尔姆的、霍赫伯格的和霍梅尔的MTP相关的MTP，它们的功效较低，但即使并非所有原假设都被拒绝，也有可能做出比拒绝断言更精确的置信断言。因此，可以选择并预先指定这样一个MTP，尽管这是以较低的拒绝功效为代价的。
