From Kernels to Mixtures

Mixture models, which include kernel estimators, are used widely to model complex densities; however, one is faced with the challenge of determining an appropriate number of components. This task often involves identifying those components that are close enough to be combined. This article introduces a new easily calculated measure of similarity between pairs of densities and illustrates its use in recursively collapsing components. This similarity measure leads naturally to a new algorithm (IPRA) for fitting mixture models sequentially. The algorithm is used to test for bumps in galaxy star velocity data and to examine MRI data.