Estimating parameters of mixtures of multivariate [formula omitted]-populations and application to classification of observations

Abstract

The problem of classifying an observation into mixtures of two multivariate t-distributions is studied when the location parameters and covariance matrices are unknown. For mixtures of two multivariate t-distributions, we propose classification rules based on the maximum likelihood estimators and Bayes estimators of the parameters. The maximum penalized likelihood estimators of the parameters are derived using some informative penalty function. We derive shrinkage estimators of the covariance matrices using a regularized parameter and propose the corresponding classification rule. The kernel density-based rule is proposed considering the diagonal matrix as a bandwidth parameter. A simulation study is carried out to compare the rules in terms of the expected probability of misclassification. Applications of the rules are described using real data sets arising in clinical studies and stock market.