在同時檢定多個假設的問題上，過去文獻著重於控制整體錯誤率(the familywise error rate; FWE)，或錯誤拒絕率(the false discovery rate; FDR)。但當多個假設的某些假設不為真時，控制整體錯誤率通常較保守且檢定力較小，因此過去文獻建議透過控制錯誤拒絕率以控制整體型Ｉ誤發生的機率，然而錯誤拒絕率或整體錯誤率的計算與假設為真的個數有關，本論文的主要目的是在估計假設為真的個數以控制整體型I誤發生的機率，同時提高檢定力。目前有不同文獻針對虛無假設為真個數的估計相繼提出各種的方法，但大部分的文獻中都是假設檢定統計量為獨立去進行估計或是在假設檢定統計量相關下去估計錯誤拒絕率。本文將檢定統計量視為相依的情況下對文獻中提出的方法進行改進，並以統計模擬方法估計虛無假設為真的個數及計算其標準誤(standard deviation)、均方差(mean square error; MSE)來評估各方法的表現。

　　In the multiple testing problem, the literatures emphasize the familywise error rate (FWE) or the false discovery rate (FDR). When some hypotheses are not true, the familywise error rate controlling procedures tend to be more conservative and be less power in testing. Thus, to estimate the number of true null hypotheses in multiple testing is important in order to control the overall type I error rate and simultaneously to improve the power. There are some literatures proposed some methods to estimate the number of true null hypotheses at present; however, most of methods in literatures estimate the number of true null hypotheses under the independent assumption. This paper is presented to improve the methods in literatures under the assumption of dependency for the test statistics. A simulation study is conducted to evaluate the performances of proposed procedure by estimating the number of true null hypotheses, standard deviations, and the root mean square errors of the estimations.

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