臺灣博碩士論文加值系統

最近的應用，特別是在基因組學和影像學，要求在同時測試大量的
假設檢定問題。偽發現率(FDR)已被建議，並承認作為一個強有力的標準在此種情況之下。偽發現率的逼近，如局部偽發現率(lfdr)已被提出和合理利用於兩群模型(two-groups model)之下，例如Efron (2007a)。在此論文中，我們利用邊緣化(marginalization)的方法推廣兩群模型，並且在其架構下，探討偽發現率及局部偽發現率的合理性。當中亦關聯偏斜常態分布(skew-normal)。

Recent applications, particularly in genomics and imaging, call for testing large number
of hypothesis tests at the same time. The False Discovery Rate (FDR) has been proposed
and recognized as a powerful criterion in these contexts. Approximations of FDR such as
local false discovery rate (lfdr) has been proposed and justified using two-group models,
for example Efron (2007a). A generalization of two-group models is proposed. Under this
framework, we study various approximations of false discovery rate and their validity.
The connection with skew normality is also addressed.

1 Introduction 1
2 FDR and lfdr under hypothesis testing framework 7
2.1 Simple hypothesis testing problems . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Composite hypothesis testing problems . . . . . . . . . . . . . . . . . . . . 16
3 Estimating FDR and lfdr 29
3.1 Two-groups model-based estimation . . . . . . . . . . . . . . . . . . . . . . 29
3.2 Marginalization-based estimation . . . . . . . . . . . . . . . . . . . . . . . 47
4 Conclusion and Discussion 65
Appendix 69
1.1 Simple hypothesis testing problems simulation . . . . . . . . . . . . . . . . 69
1.2 One-sided hypothesis testing problems simulation . . . . . . . . . . . . . . 71
1.3 Two-sided hypothesis testing problems simulation (based on the two-groups
model) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
1.4 Two-sided hypothesis testing problems simulation (based on marginalization) 76

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