期刊名称：Sankhya. Series A, mathematical statistics and probability
印刷版ISSN：0976-836X
电子版ISSN：0976-8378
出版年度：2003
卷号：65
期号：03
出版社：Indian Statistical Institute
摘要：The bootstrap density plot (histogram) of ``mean $-$ trimmed mean'' for a suitable trimming number is proposed as a nonparametric graphical tool for detecting outlier(s) in a data set. This plot is multimodal in the presence of outliers. As an exploratory data analysis tool, this method can be applied to data sets from a wide range of distributions, and it is quite effective in detecting outlying values in data sets with small portion of outliers. The main strength of this plot lies in its ability to incorporate heavy or short tailedness of the data in outlier detections and its effectiveness for outlier detection in multivariate settings where only few tools are available. We start with the univariate case, and extend the method to multivariate outliers. We also develop a quantitative index (called bootlier index) to assess the bumpiness of a bootlier plot. In addition, some theoretical results are presented which explain how the multimodality in the bootlier plot is caused by outlier(s) in the sample.
