2003, Volume 65, Pt. 3, 532--559

Bootlier-Plot --- Bootstrap Based Outlier Detection Plot


KESAR SINGH and MINGE XIE, Rutgers University, Piscataway, New Jersy, USA

SUMMARY. 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.

AMS (1991) subject classification. 62G09, 62G35, 62G20.

Key words and phrases. Bootstrap method, outliers, multi-dimensional outliers, Jackknife method, robust statistic.

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