When testing the presence of (k+1) clusters versus the presence of k clusters, Hardy considers a stationary Poisson point process in some domain D⊂ℝd which is the union of k disjoint convex compact domains Di (i=1, 2, …, k) (k fixed). In order to derive a stopping rule for determining the ‘optimal’ number of clusters present in a given set of data, Hardy proposed the likelihood ratio test for H0:v=k versus H1:v=k+1. However, one can see that k (the number of components) is not a parameter of the model. The goal of this small note is to give a more accurate formulation of this test, which is based on the concept of finite mixture models.
