淡江大學覺生紀念圖書館 (TKU Library)
進階搜尋


下載電子全文限經由淡江IP使用) 
系統識別號 U0002-1506200621294200
中文論文名稱 從可交換隨機變數找信賴區間
英文論文名稱 Finding confidence interval under exchangeability
校院名稱 淡江大學
系所名稱(中) 數學學系碩士班
系所名稱(英) Department of Mathematics
學年度 94
學期 2
出版年 95
研究生中文姓名 劉家豪
研究生英文姓名 Chia-Hao Liu
學號 693150558
學位類別 碩士
語文別 中文
口試日期 2006-06-01
論文頁數 28頁
口試委員 指導教授-鄭惟厚
委員-趙晨慶
委員-張玉坤
中文關鍵字 排列檢定  信賴區間 
英文關鍵字 permutation tests  confidence interval 
學科別分類 學科別自然科學數學
中文摘要 在一般用參數檢定(parametric tests)估計未知位置參數時,利用雙尾檢定找未知參數的接受域(acceptance region),就可以得到信賴區間(confidence interval),我們將這個概念用在從排列檢定(permutation tests)找信賴區間。對於一般的參數檢定問題,通常只要找到樞紐(pivot)統計量,再利用簡單的代數就能找到信賴區間,但是從排列檢定找信賴區間,狀況卻複雜許多。

於單一樣本的情況下,排列檢定是將觀測值減去原始假設下的參數之後,討論所有可能的正負號分配情況,得此假設下的排列分布,再根據此排列分布來判斷是否接受原始假設。不過每減去不同的參數值,所對應的排列分布也必須重新計算,這使得計算過程極為繁瑣。本文討論的是不同信心水準信賴區間所對應的條件,並試圖用較精簡的方式將這些條件表示出來以利應用。另外並提供了程式,在 n=7 的情況下可直接利用此程式找出信賴區間。

我們也利用找出的條件檢驗了來自標準常態分布、均勻分布及標準雙指數分布的樣本,檢測從何者抽出的樣本較容易滿足信心水準 90% 以上的信賴區間之條件。另外,若樣本來自連續對稱的單峰分布,在相同「位置間距」下,也討論了「不對稱位置」的區間和「對稱位置」的區間何者較長。
英文摘要 In general case of parametric tests,we can usually find the confidence interval of an unknown location parameter via the acceptance region of a two-tail test. In this paper,we use this same concept to find confidence interval based on permutation tests. But in parametric tests, 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 much more complex.

To carry out a permutation test on a center of symmetry,we subtract the parameter under consideration from each of the observations to get the permutation distribution,and then decide whether to accept the null hypothesis based on the permutation distribution. However,the computing process is very tedious,because the permutation distribution has to be recomputed every time we subtract a different parameter. We discuss conditions under which there exist confidence intervals corresponding to different confidence coefficients. We also try to find ways to simplify these conditions to make applications easier. In the case of n=7 ,a program is supplied for finding confidence intervals.

We compared samples from standard normal,uniform and standard double exponential distribution to find out which one satisfies the conditions for existence of 90% (and above) confidence interval more often. We also compared the length of intervals whose end points have "asymmetric locations" with those that have "symmetric locations" and obtained a result for a special case.
論文目次 1.序言...........................................1
2.文獻回顧.......................................3
3.從排列檢定找信賴區間...........................4
3.1.如何從樣本尋找信賴區間(confidence interval)..4
3.2.信賴區間的檢查條件...........................8
3.3.n=8之條件討論...............................11
4.Walsh average 轉換............................13
5.「對稱」與「不對稱」區間長度探討..............18
6.程式..........................................24
7.結論..........................................25
參考文獻........................................26
附錄............................................27
程式碼..........................................27

表目錄
1.n=5下所有可能的條件............................7
2.各條件所成的信賴區間與信心水準的關係..........15
參考文獻 [1]Arnold,H.J(1964),
Permutation support for multivariate techniques
Biometrika 51, pp65-70.

[2]Fisher,R.A(1936),
Coeffcient of racial likeness and the future of craniometry
J.Roy.Anthrop .Soc 66, pp57--63.

[3]Good,Phillip(2000).
Permutation tests.
Springer-Verlag.

[4]Hubert,L.J.and Levin,J.R.(1976).
Inference models for categorical clustering.
Psych Bull 83, pp878-887.

[5]Hubert,L.J.and Levin,J.R.(1976).
General statistical framework for assessing categorical clustering in free recall.
Psych Bull 83, pp1072-80.

[6]Mielke,P.W.Jr.(1986).
Non-metric statistical analysis:some metric alternatives.
JSPI 13, pp377-387.

[7]Randles,R.H. and Wolfe.
Introduction to the theory of Nonparametric Statistics.
John Wiley.

[8]Robinson,J.(1987).
Nonparametric confidence intervals in regression:The bootstrap randomization methods.New Perspectives in Theoretical and Applied Statistics.M.Puri,J.P.Vilaplana,and W.Wertz.Eds.
John Wiley and Sons, pp243-256.

[9]John Ludbrook and Hugh Dudley(1998).
Why Permutation Tests Are Superior to t and F Tests in Biomedical Research.
The American Statistician 52, pp127-132.

[10]高春元(2005).
排列檢定與信賴區間(On discussion of confidence interval based on permutation tests).
(淡江大學數學學系碩士班碩士論文).
論文使用權限
  • 同意紙本無償授權給館內讀者為學術之目的重製使用,於2006-06-27公開。
  • 同意授權瀏覽/列印電子全文服務,於2006-06-27起公開。


  • 若您有任何疑問,請與我們聯絡!
    圖書館: 請來電 (02)2621-5656 轉 2281 或 來信