The partitioning principle: a powerful tool in multiple decision theory
The partitioning principle: a powerful tool in multiple decision theory
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DOI：
10.1214/aos/1031689023
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发表时间：
2002-08
影响因子：
4.5
通讯作者：
BY H. Finner;K. Strassburger
中科院分区：
文献类型：
--
作者：
BY H. Finner;K. Strassburger
用于构造控制多电平a的强大的多测试过程的第一一般原理和当前技术状态是所谓的闭合原理。在这篇文章中，我们介绍了另一个强大的工具，用于构建多个决策过程，特别是用于构建多个测试过程和选择过程。这个工具是基于参数空间的分区，并将被称为分区原则（PP）。在本文的第一部分中，我们回顾了多假设检验的基本概念，并讨论了当前理论的一个轻微的概括。在第二部分中，我们提出了PP的各种变体，用于构造多个测试过程，这些是一般PP（GPP），弱PP（WPP）和强PP（SPP）。它将被证明，根据基本的决策问题，PP可能会导致更强大的测试程序比正式应用的封闭原则（FCP）。此外，更复杂的SPP可能比WPP更强大。基于测试和选择之间的二元性，PP也可以用于构建更强大的选择程序。在论文的第三部分中，对FCP、WPP和SPP进行了应用和比较。
A first general principle and nowadays state of the art for the construction of powerful multiple test procedures controlling a multiple level a is the so-called closure principle. In this article we introduce another powerful tool for the construction of multiple decision procedures, especially for the construction of multiple test procedures and selection procedures. This tool is based on a partition of the parameter space and will be called partitioning principle (PP). In the first part of the paper we review basic concepts of multiple hypotheses testing and discuss a slight generalization of the current theory. In the second part we present various variants of the PP for the construction of multiple test procedures, these are a general PP (GPP), a weak PP (WPP) and a strong PP (SPP). It will be shown that, depending on the underlying decision problem, a PP may lead to more powerful test procedures than a formal application of the closure principle (FCP). Moreover, the more complex SPP may be more powerful than the WPP. Based on a duality between testing and selecting PPs can also be applied for the construction of more powerful selection procedures. In the third part of the paper FCP, WPP and SPP are applied and compared in some examples.