臺灣博碩士論文加值系統

控制整體的型一誤差一直是進行多個統計檢定時很重要的議題。對於型一誤差的定義有族型一誤 (familywise error rate) 或是偽陽率 (false discovery rate),
有許多相對應的檢定準則可以控制FWER 或 FDR,但在錯誤虛無假設的個數增加時,控制FWER或 FDR的方法都會趨於保守。Benjamini 和 Hochberg (2000)
提出以正確虛無假設的個數來調整原有的控制FWER或 FDR的方法,用以提高檢定的控制型一誤的能力及提高檢定力。為有效始用調整檢定的檢定方法,
本論文套用Parker 及 Rothenberg (1988) 的混合模型,假設多重比較中每一個檢定所產生的檢定統計量的值,或每一個檢定所產生的P值會服從混合模型,
利用混合模型中的參數估計來預測正確虛無假設的個數,而混合模型的參數估計利用EM演算法加以迭代求得。為正確知道配適混合模型的成分個數,
用重抽方法及Cramer-von Mises檢定來選取最恰當的成分個數。文中以不同情況的資料型態加以模擬,最後再使用白血病(Leukemia)患者的基因表現資料對上述方法進行實證討論。

Controlling the overall Type I error is an important issue in the
multiple hypotheses. Familywise error rate (FWER)or false
discovery rate (FDR) are commonly used definitions for Type I
error and controlling procedures are proposed accordingly.
However, when the number of true alternative hypotheses
increases, the ability in controlling Type I error and the power
of the controlling procedures reduce. Benjamini and Hochberg
(2000) proposed a adaptive procedure that incorporates the number
of true null hypotheses and is shown to have the ability in
controlling the error and have higher power. To use this adaptive
procedure, this thesis adapts the mixture model proposed by
Parker and Rothenberg (1988) to model the test statistics or the
corresponding $p$ values from the multiple hypotheses. The model
parameter can be used to estimate the number of true null
hypotheses. Furthermore, the bootstrap type likelihood ratio test
and Cramer-von Mises test are used to assess the number of
components in the mixture model. Simulations are performed to
evaluate the feasibility of this model. Gene expression data for
leukemia patients are used to illustrate the method.

1. 序論 1
2. 研究方法 5
2.1 定義混和模型 ...............................5
2.2 利用EM演算法求混合模型參數最大概似估計值 ...7
2.2.1 常態混合模型的參數最大概似估計量 .....11
2.2.2 Beta混合模型的參數最大概似估計量 .....12
2.3 混合模型選取適當的成分個數 ................14
2.4 混合模型中參數意義的解釋 ..................17
3. 統計模擬 19
3.1 模擬環境的設定 ............................19
3.2 模擬參數的設定 ............................22
4. 統計模擬結果 24
4.1 常態混合模型的模擬結果 ....................25
4.2 Beta混合模型的模擬結果 ....................26
5. 白血病患者基因表現資料分析 51
5.1 利用 Beta分配混合模型進行估計 .............51
5.2 利用常態分配混合模型進行估計 ..............54
6. 結論 57
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