Penalized partial likelihood for sequential order selection

We have previously shown that partial likelihood estimation of finite normal mixtures (FNM) yields very efficient estimators and hence provides a very attractive solution for real-time signal processing. Order selection, however, is a very important factor affecting the overall performance. We address the problem of order selection for the FNM model in applications requiring sequential processing. We pose the problem as the joint determination of the system memory and the observation vector dimension which together determine the number of mixture components. We define penalized partial likelihood as the information theoretic criterion for order selection and propose a sequential order selection procedure. We consider channel equalization as an example, an application for which FNM provides a perfect match to the data generation mechanism and hence is a particularly attractive solution. We study examples in channel equalization showing the effectiveness of the approach and discuss its properties.