由離群值建構無母數檢定

Abstract

離群值在統計推論中一直居相當重要的地位。在穩健性統計中我們把資料分成含離群值的一群與非離群值的一群，然後再用非離群值的一群建造統計推論方法。 最近人們(Tomlins et al. 2005, Science)發現離群值資料在變異基因的選取上具 有相當的功效。其後， Tibshirani 及Hastie(2007, Biostatistics) 及Wu(2007, Biostatistics)提出用離群值之和及Chen, Chen及Chang(2010, Biometrika)提出用離 群值之平均來做統計推論其中後者導出統計量的分配。離群值之和或平均祇能驗 出離群值分配的集中趨勢卻無法檢驗此分配之其他特徵(如變異等)。我們將提出離 群變異及離群百分比用來檢驗離群值分配之變異及產生離群值之機率用來檢驗分 配是否異動。大樣本分配及檢力之研究也將予以報告。

Detection of Outlier Data has long been important for statistical inferences. Robust statistical inference techniques require classification of data into class of outliers and class of good data and use the good data to construct inference methods. Recently it is seen (Tomlins et al. (2005, Science)) that detection of outlier data is important in gene expression analysis. Latter, Tibshirani and Hastie (2007, Biostatistics) and Wu(2007, Biostatistics) proposed the outlier sum and Chen, Chen and Chang (2010, Biometrika) derived the distribution of outlier mean (average of outlier sum). The outlier sum or outlier mean technique can detect the shift in central tendency for the outlier distribution but not other characteristics of the outlier distribution. We propose the outlier variance and outlier proportion to measure the spreadness and outlier probability as alternatives for distributional shift detection. We will develop their large sample theory and perform simulations to verify the power when there is distributional shift.