Envelope plots of ordered Mahalanobis distances: uses and efficient generation

Systematic departures from a reference sampling scheme, such as multivariate normality, can affect all the observed ordered Mahalanobis distances (OMDs) – not just a few extreme values – causing distinctive changes to their overall pattern. Envelope OMD plots provide a useful framework against which to ‘read’ such changes, often suggestive of further, confirmatory analyses. Illustrative examples include heavy-tailed and skew distributions and the presence of (clusters of) outliers. The exact distributions involved being intractable, the above framework is found by simulation. Fast, accurate approximations to it are also developed for use when such simulation is computationally prohibitive.