無母數離群平均之基因分析

Abstract

離群平均用於檢定整個分配的偏移時有不錯的檢定力，然而部分分配偏移時放大了離群平均值的變異數，導致檢定力大幅下降，而這部分分配偏移的情況在癌症的研究上頻繁可見。傳統的統計方法使用好的資料來做統計推論，而離群平均是利用離群值做統計推論，二者在觀念上有很大的不同。我們從兩個觀點來思考無母數離群平均值的研究，首先推導離群平均之漸進分配，建立 水準檢定與計算 值，接著針對離群值的判定原則，推論檢定力和漸進變異數之間的關係。

The outlier mean has a reasonable power when the distribution is in a location shift, however, its power is remarkably reduced when he distribution is shifted on only a small fraction of observations, due to large asymptotic variances, while this happen frequently in the cancer study. We consider the study of the nonparametric outlier mean (outlier sum) in two aspects. First, the development of asymptotic distribution for establishing a level test or computing value is established. Second, concept of using outliers for statistical inferences may be treated differently from the classical statistical inferences that construct rules based on good data. We study the relation between powers and asymptotic variances of outliers means aiming at drawing principles for choosing outliers - based inference techniques.