臺灣博碩士論文加值系統

在同時檢定多於一個統計假設(多重檢定)的時候, 研究者遭遇到的重要課題之一就是力求在控制型一誤差率(錯誤拒絕率)的同時, 使得檢定力(正確拒絕率)最高。 自Benjamini and Hochberg 於1995 年提出以False Discovery Rate (FDR) 控制多重檢定問題的型一誤差率後, 近年來許多學者們提出新的檢定方法,使得型一誤差控制在FDR下之餘, 也提供較大的檢定力。 然而, 處在不斷有新方法追求更高的檢定力的當下, 在各法中檢視其專一性, 敏感性等檢定結果正確率與False Non-Discovery Rate (FNDR) , Family-Wise Error Rate (FWER) 等檢定產生的誤差率也是刻不容緩的事。 本研究將以各控制FDR檢定方法為基礎, 在突破檢定方法的檢定統計量間獨立等統計假設與討論其他如統計假設個數,樣本數, 真實虛無假設比例等相關參數的更動下, 以統計模擬方法綜合比較其專一性, 敏感性, FNDR, FDR, FWE等, 並以各種角度來檢視各法適用時機, 以求自其中求得修FDR檢定方法的新方向。

One of the important tasks researchers would encounter in multiple testing is to control the Type I Error Rate at the desired level and to maximize the power at the same time. Since Benjamini and Hochberg (1995) proposed using False Discovery Rate (FDR) to control the Type I Error Rate, researchers have proposed many new FDR controlling procedures that are more powerful in specific circumstances. Although new procedures have been developed constantly for higher power, evaluating the rate of correct testing result, such as specificity, sensitivity, and the rate of wrong testing result, such as False Non-Discovery Rate (FNDR), Family-Wise Error Rate (FWER), also demand immediate attention. On the basis of seven FDR controlling procedures, this thesis presents Monte Carlo simulations to evaluate these testing procedures using specificity, sensitivity, FNDR, FDR and FWER under various related parameters, such as number of null hypothesis, sample size, proportion of true null hypotheses. Moreover, the situation when test statistics are correlated is considered as well. These seven testing procedures are evaluated in various aspects. Simulation results reveal that different testing procedures perform differently in specificity, sensitivity, FNDR and FWER. Researchers should choose an appropriate testing procedure based on their specific research aim.

第一章 前言 9
第二章 研究方法 11
2.1 背景 11
2.2 多重假設檢定方法 12
第三章 統計模擬 16
3.1 虛無假設的設定與資料生成方式 16
3.2 檢定統計量的設定與p值的計算 19
3.3 研究參數設定 20
第四章 模擬結果討論 22
4.1 檢定結果U,V,S,T,R,W討論 22
4.2 單一參數變動討論 29
4.3 三參數變動討論 37
4.4 sigma1與sigma2的討論 58
4.5 特定的參數設定變動討論 64
第五章 結論 68
參考文獻 72
附圖 74

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