On Masking and Swamping Robustness of Leading Outlier Identifiers for Univariate Data

In the wide-ranging scope of modern statistical data analysis, a key task is identification of outliers. In using an outlier identification procedure, one needs to know its robustness against masking (an “outlier” is undetected) and swamping (a “nonoutlier” is classified as an “outlier”), possibilities which can come about due to the presence of outliers. Study of these issues together is necessary but complex. Recently, Serfling and Wang (2012) developed a general framework providing foundations, tools, and criteria applicable in any data space. Application of this framework to particular outlier identifiers in particular types of data space requires, however, additional development of a nature specialized to the chosen setting. The present paper applies the general framework to the case of univariate data and evaluates masking and swamping robustness for two leading outlier identifiers, scaled deviation outlyingness and centered rank outlyingness. Our results shed new light on the choice between (Median, MAD) and (trimmed mean, trimmed standard deviation) in defining scaled deviation outlyingness. Also, our findings explain how the boxplot, a leading descriptive tool, acquires its excellent robustness by incorporating a scaled deviation outlier identification component alongside its quantile-based description of the central part of a data set. AMS 2000 Subject Classification: Primary 62G35 Secondary 62-07