The Comparative Efficacy of Some Combinatorial Tests for Detection of Clusters and Mixtures of Probability Distributions

Assume that nq-dimensional data points have been obtained and subjected to a cluster analysis algorithm. A potential concern is whether the resulting clusters have a “causal” interpretation or whether they are merely consequences of “random” fluctuation. In previous reports, the asymptotic properties of a number of potentially useful combinatorial tests based on the theory of random interval graphs were described. In the present work, comparisons of the asymptotic efficacy of a class of these tests are provided. As a particular illustration of potential applications, we discuss the detection of mixtures of probability distributions and provide some numerical illustrations.