多重假設檢定問題下t統計量的行為

Abstract

在基因晶片資料的分析中，通常我們會同時考慮數以千計或數萬個t-檢定統計量用以區別個別基因之重要性。在這種多重檢定的過程中，這些檢定統計量常常會存在一些相關性，因此他們的分配將不會是一般的常用的t分配。在這篇論文，我們討論這許多t-檢定統計量的分配不為t分配的可能原因。這些可能原因分別是不同基因間存在某些相關，不同基因晶片間存在某些相關，以及基因表現不是來自常態分配的假設。在分析的過程中，我們會考慮一些特殊模型並且運用統計模擬分析之技巧來探討這些可能原因的影響。

關鍵字：多重檢定過程,t-檢定量,t-分配

Microarray data has been studied widely, with thousands or even millions of test statistics ti's to be considered at the same time. These test statistics ti's are correlated or not regular distributed on multiple testing procedure. In this paper, we discussed three possible reasons for the distribution of test statistics ti's differing from t-distribution. The three reasons are correlation between genes, correlation among microarrays, and various distribution assumptions. Then, we consider several models and conclude that correlation among microarrays and various distribution assumptions are most important effects which make the distribution of test statistics ti's differing from t-distribution. Key words: Multiple testing procedure, t-statistics, t-distribution.