從排列檢定找信賴區間

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Title:	從排列檢定找信賴區間
Other Titles:	On Confidence Intervals Based on Permutation Tests
Authors:	鄭惟厚
Contributors:	淡江大學數學學系
Keywords:	排列檢定;信賴區間;無母數方法;permutation test;confidence interval;nonparametric method
Date:	2004
Issue Date:	2009-03-16 12:51:13 (UTC+8)
Abstract:	排列檢定的概念很早以前就有人用了。它最大的特色在於假設極少，基本上檢定結果只根據數據本身而決定。從此角度看，可說它是最「自然」的方法。而因為背景假設少，對應用的人來說，應該比較容易理解，也比較不需擔心用得是否恰當。從統計角度來看，排列檢定的主要價值在於其應用範圍極廣，對大部分的檢定, 都可找到對應的排列檢定，而此排列檢定常有同樣甚至更好的檢力。有很多時候只做檢定並不夠，我們會需要估計未知參數。在一般檢定的架構下，從對於未知參數的雙尾檢定的接受域，我們就可得到參數的信賴區間。對於排列檢定，這個概念仍然適用，然而要實際找到信賴區間，一般來說情況要複雜得多。針對這個問題，似乎不見系統性的討論，但若沒有較具系統性的方法可用，必定影響許多人的使用意願。本計劃的目的，就是要試圖找尋從排列檢定找信賴區間的系統性方法。Permutation tests have been in use for a long time. What characterizes it is the fact that there is very little assumption behind it. And because of this fact, it should be easier to understand, and one does not need to worry too much about the appropriateness when one applies it. From the statistics point of view, permutation tests have very wide application and yet at the same time, very competitive powers. Sometimes a test is not enough, we might need to estimate our parameter. Under the usual parametric test situation, a confidence interval can usually be found easily from the acceptance region of a two-tailed test. This is not the case with permutation tests, it is often much more complicated. There seems to be very little discussion on the subject. And without a systematic method of finding the confidence interval, people will be reluctant to use this method. This project is aimed at finding this systematic method.
Appears in Collections:	[Graduate Institute & Department of Mathematics] Research Paper

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