On Regularity of Multivariate Datasets

The authors propose grade irregularity measures (function-valued and numerical) for bivariate probability tables and apply them to evaluate irregularity of non-negative multivariate datasets. The results of a simulation study performed on multinormal and multiexponential data are presented and displayed graphically. This study serves not only to illustrate behavior of the irregularity measures but also to observe that in sufficiently regular datasets linear multivariate prediction is close to optimal.