離群值比例之基因分析

Abstract

藉由偵測病體樣本中的離群值而找出具有影響力的基因已是一種非常新且重要的基因分析方法。透過離群和或是離群平均可以偵測出離群資料中的集中趨勢是否有所改變，但是卻無法偵測出偏度等其它特徵量數。因此，我們希望可以提供一個容易實行且有較高檢定力的統計檢定，以作為基因分析的另一項替代選擇方法。我們將提出離群值比例的觀點，以離群值比例的近似分配為基礎，發展出一項統計檢定。此外，我們也將更進一步地比較離群值比例和離群平均兩者的檢定力表現。而為了避免估計尾端機率點的密度函數之困難，進而造成檢定力較低的缺點，因此我們將採用經驗分位數當作切點。

Discovering the influential genes through the detection of outliers in samples of disease group subjects is a very new and important approach for gene expression analysis. The outlier sum or outlier mean technique can detect the shift in central tendency for the outlier data but not other characteristics such as spreadness or others for the outlier data. It is desired to provide a test that is easy to implement and efficient in power performance as an alternative tool for gene expression analysis. We propose the concept of outlier proportion for developing a test based on asymptotic distribution of this statistics. We further compare it with the outlier mean for their power performances. To avoid the inefficiency in estimating densities at tail quantiles involved in estimation of outlier proportion variance, we further consider applying the empirical quantile as the cutoff point for an alternative outlier proportion based test which shows satisfactory role in gene expression analysis from the point of power performance.