An Efficient Algorithm to Simulate Outliers With Known Mahalanobis Distances for Normal and Nonnormal Data

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Abstract

Outliers have a well-documented, long history in statistical research, given the undue impact they can have on parameter estimates, standard errors, and inferential decisions in general. Multivariate outliers can be particularly pernicious since they could appear as regular data points in lower dimensions but become outliers once a more comprehensive investigation is conducted. Simulation algorithms are therefore needed to aid researchers in documenting and testing the effect that outliers can have on their analyses. This paper extends an algorithm to simulate multivariate outliers with a known Mahalanobis distance. A proof of concept is presented, and an extension will be offered to generalize this method to families of multivariate, non-normal densities.

Authors

• Yijun Cheng, University of Washington

• Oscar L. Olvera Astivia, University of Washington