基因表現分析之穩健回歸估計量

Abstract

對基因表現分析來說，經由偵測疾病組樣本的離群值來發現對其有影響力的基因，是一個很新而且很重要的方法。不幸的是，我們在文獻裡找到，為了建構回歸模型而發展出的離群值最小平方法估計量，它的影響函數(influence function)無法限制住對獨立變數的影響。為了建構線性回歸模型，我們用Mallow's type 離群值有界影響最小平方法估計量及離群值回歸分位數的漸進分布，產生出一個影響函數(influence function)在獨立變數空間是有界的統計方法。由蒙地卡羅模擬比較均方差的結果顯示，當過失誤差(gross error)在獨立變數空間發生時，有界影響的估計量比無界影響的更有效。

Discovering the infl?uential genes through the detection of outliers in sam?ples from disease group subjects is a very new and important approach for gene expression analysis? Technique of outlier least squares estimator for re?gression model has been found in literature that? unfortunately? its in?fluence function can not limit the e?ect of independent variables? We present as?ymptotic distributions of the mallow?s type bounded? infl?uence outlier least squares estimator and outlier regression quantile for linear regression mod?els producing statistical techniques with infl?uence functions bounded in the space of independent variables? Monte Carlo simulations comparing mean squared errors show that the bounded? infl?uence ones are more effcient than the unbounded? infl?uence ones when gross errors occur in the independent? variable? space?