Research Projects

This project aims to investigate the inference on parameters in the discriminant function for multivariate skewed distributions and directional distributions. The discriminant analysis will be conducted for populations with a mixture of multivariate skew-normal and unknown parameters. Maximum posterior and maximum penalized likelihood estimators (PLEs) will be derived for the mixture of multivariate skew-normal distributions. The consistency property of PLEs will be studied. A plug-in classification rule will be proposed based on MLEs, maximum posterior estimators, PLEs, shrinkage estimators, and kernel density-based classifiers. The probability of misclassification for the rules will be estimated. Non-rotationally symmetric axial data will be classified into angular central Gaussian distributions. Bayes estimators and shrinkage estimators will be used to classify non-rotationally symmetric axial data. The likelihood ratio-based rule and kernel density classifier will be proposed for classifying observations. The influence of observations on the total probability of misclassification will be calculated using partial influence function and influence function. Robust estimators of parameters will be derived, proving to be better than existing estimators in terms of risk under certain conditions. The project will also study the problem of estimating discriminant coefficients based on multivariate skewed distributions with unknown parameters.