Matching model information content to data information

Given data drawn from an unknown probability distribution one is often interested in building a model of the data. This problem occurs frequently in the area of statistical pattern recognition. Often one needs not only a good functional estimate of the distribution, but a model that matches the complexity of the data as well. Techniques for building nonparametric variable bandwidth mixture models are developed in this dissertation. In addition, new visualization techniques to study the time evolution of these mixture models during likelihood maximization are also presented. The Akaike Information Criterion and the Minimum Description Length information measures are used to help determine appropriate model complexity. The consistency and algorithmic complexity properties of the new estimators are studied using Monte-Carlo simulations. The new estimators are applied to texture features extracted from a mammogram. The ability of the estimators to appropriately model the modal structure of the mammographic features is studied.