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系統識別號 U0026-0812200911280265
論文名稱(中文) 多重檢定中估計虛無假設為真的個數之研究
論文名稱(英文) A Nonparametric Approach to Estimate the Number of True Null Hypotheses in Multiple Testing
校院名稱 成功大學
系所名稱(中) 統計學系碩博士班
系所名稱(英) Department of Statistics
學年度 93
學期 2
出版年 94
研究生(中文) 趙文章
研究生(英文) Wen-Chang Chao
學號 r2692115
學位類別 碩士
語文別 英文
論文頁數 69頁
口試委員 指導教授-劉仁沛
口試委員-溫淑惠
指導教授-馬瀰嘉
中文關鍵字 整體錯誤率(FWER);錯誤拒絕率(FDR);多重比較方法;P值 
英文關鍵字 Familywise error rate (FWER); False discovery ra 
學科別分類
中文摘要 在同時檢定多個假設的問題上,過去文獻常使用控制整體錯誤率(the familywise error rate; FWER),及錯誤拒絕率(the false discovery rate; FDR)的方法,其中多重比較方法最常被使用來控制整體型I誤發生的機率。當多個假設的某些假設不為真時,利用控制整體錯誤率的方法通常較保守(在單獨比較問題上型I誤發生的機率小於既定的顯著水準)而且具較小的檢定力,欲改進多個假設的檢定力,方法之一為估計假設為真的個數。
本文利用McNemar檢定方法推導出一無母數估計方法,並利用統計模擬方法以均方差(mean square error; MSE)來評估所提出方法的表現,並且與Hsueh等人於2003年所提出之估計方法,在一定的顯著水準下,比較FWER和FDR的大小。最後利用一電腦微晶片資料(microarray data set) 舉例說明此方法的應用。


英文摘要 The problem is important for controlling the familywise error rate (FWER) or the false discovery rate (FDR) in testing a large number of hypotheses. The classical multiple comparison procedures aim to control the probability of type I error in families of comparisons. When some hypotheses are not true, the classical FWER-controlling procedures tend to have less power and less error rate than the significance level. To improve the power, an approach is to estimate the number of true hypotheses in multiple testing.
A nonparametric approach based on the McNemar test is presented. A simulation study is conducted to evaluate the performance of proposed procedure and the methods proposed by Hsueh et al. (2003). The appropriateness of criterion is illustrated with an example from a microarray data set.


論文目次 Chapter 1 Introduction 1

Chapter 2 Literature Review 3
2.1 Schweder and Spjψtvoll’s Method 5
2.2 Storey’s Method 7
2.3 Benjamini and Hochberg’s Lowest Slope Method 7
2.4 Mean of Differences Method 8
2.5 Least Squares Method 9

Chapter 3 Proposed Methods 11
3.1 The Problem in Literature 11
3.2 Proposed Method 12
3.2.1 Average Ordered P-value method 12
3.2.2 Equal Quality Method 13
3.2.3 The McNemar Test (Plus) 14
3.2.4 The McNemar Test (Minus) 16
3.2.5 The McNemar Test (Average) 16
3.3 Applying to Multiple Testing Procedure 17
3.4 Numerical Example 18

Chapter 4 Simulation Study 24
4.1 Simulation procedure 24
4.1.1 Two-sided Test 24
4.1.2 One-sided Test 26
4.2 Simulation Results 30

Chapter 5 Discussion 33
References 34
Appendix 36
參考文獻 1.Benjamini, Y., Hochberg, Y. (1995). Controlling the false discovery reat: a practical and powerful approach to multiple testing. J. R. Statist. Soc. B 57:289-300.
2.Benjamini, Y., Hochberg, Y. (2000). On the adaptive control of the false discovery rate in multiple testing with independent statistics. J. Educ. Behav. Statist. 25:60-83.
3.Benjamini, Y., Liu, W. (1999). A step down multiple hypotheses testing procedure that controls the false discovery rate under independence. J. Statist. Plann. Inference 82:163-170.
4.Cox, D. R. (1977). The role of significance tests. Scand. J. Statist. 4, 49-70.
5.Guo YL, Chang HC, Tsai RH, Huang JC, Li C, Young KC, Wu LW, Lai MD, Liu HS, Huang W. (2002). Two UVC-induced Stress Response Pathways in HeLa Cells Identified by cDNA Microarray. Environ Mol Mutagen 40, 122-128.
6.Hochberg, Y., Tamhane, A. C. (1987). Multiple Comparison Procedures. New York. John Wiley & Sons.
7.Hsueh, H. M., Chen, J. J. and Kodel, R. L. (2003). Comparison of methods for estimating the number of true null hypotheses in mulitplicity testing. Journal of Biopharmaceutical Statistics, 13, 675-689.
8.Schweder, T., Spjψtvoll, E. (1982). Plots of p-values to evaluate many tests simultaneously. Biometrika 69:493-502.
9.Saville, D.J. (1990) Multiple comparison procedure: the practical solution. American Statistician, 44, 174-180.
10.Storey, J. D. (2002). A direct approach to false discovery rates. J. R. Statist. Soc. B 64:479-498.
11.Westfall, P. H., Young, S. S. (1993). Resampling-Based Multiple Testing. New York: John Wiley & Sons.
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