Discriminant functions arising from selection distributions: theory and simulation

TL;DR

This paper explores discriminant functions based on extended skew-elliptical distributions, especially the multivariate extended skew-normal, providing theoretical insights and simulation results to evaluate classification performance and parameter estimation methods.

Contribution

It generalizes discriminant analysis to skew-elliptical distributions, develops a quadratic approximation for the extended skew-normal, and assesses the approach through simulation.

Findings

The proposed classification rule performs well in simulations.

The EM algorithm effectively estimates model parameters.

The extended skew-normal model offers more flexible data modeling.

Abstract

The assumption of normality in data has been considered in the field of statistical analysis for a long time. However, in many practical situations, this assumption is clearly unrealistic. It has recently been suggested that the use of distributions indexed by skewness/shape parameters produce more exibility in the modelling of different applications. Consequently, the results show a more realistic interpretation for these problems. For these reasons, the aim of this paper is to investigate the effects of the generalisation of a discrimination function method through the class of multivariate extended skew-elliptical distributions, study in detail the multivariate extended skew-normal case and develop a quadratic approximation function for this family of distributions. A simulation study is reported to evaluate the adequacy of the proposed classification rule as well as the performance of the EM algorithm to estimate the model parameters.