排列檢定與信賴區間

On discussion of confidence interval based on permutation tests

高春元(Chun-Yuan Kao)

指導教授 ： 鄭惟厚

淡江大學/理學院/數學學系碩士班/碩士(2005年)

https://doi.org/10.6846/TKU.2005.00194

摘要

在一般parametric架構下估計未知位置參數時,從對於未知參數的雙尾檢定的接受域(acceptance region),我們就可以得到參數的信賴區間。對於排列檢定,這個概念仍然適用。
然而在實際找參數的信賴區間時,一般來說比parametric檢定所用的方法要複雜得多。
因為在一般parametric的情況下,通常未知參數直接出現在樞紐量(pivot)當中,我們只要找出適當的機率式子,再利用簡單的代數,
就可得出信賴區間。然而要從排列檢定找出信賴區就複雜許多。以單一樣本的位置參數來說,在做排列檢定時,首先要把樣本中每個數據減去原始假設下的參數值,
找出其對應的排列分布(permutation test),如此才能知道能否接受該原始假設,然而處理起來相當麻煩的原因是每減掉一個不同參數值,其對應的排列分布就要重新排列過才可以得知。
本篇論文的內容就在討論如何從排列檢定的接受域來找出信賴區間,希望能找出一些系統性的結論。

關鍵字

排列檢定 ； 信賴區間

並列摘要

Under general parametric framework,we can find the confidence interval of an unknown location parameter via the acceptance region of a two-tail test .This concept can also be used in permutation tests,but it is a lot more complex to find confidence interval.Because in parametric case,the unknown parameter usually appears in the pivot and we can find the confidence interval via simple algebra. Yet in the case of permutation tests,the situation is different.
In the first step of carrying out a permutation test on a single sample for the location parameter,we subtract the parameter under consideration from each of the observations, and then decide whether to accept the null hypothesis according to the permutation distribution which is formed by all possible rearrangements of
these differences.However the permutation distribution will change every time we subtract a different parameter.
This thesis is discussing how to find the confidence interval by acceptance region via permutation test, and we try to find some systematic conclusions.

並列關鍵字

permutation tests ； confidence interval

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