A best linear threshold classification with scale mixture of skew normal populations

Abstract

This paper describes a threshold classification with $$K$$ K populations whose membership category is associated with the threshold process of a latent variable. It is seen that the optimal procedure (Bayes procedure) for the classification involves a nonlinear classification rule and hence, its analytic properties and an efficient estimation can not be explored due to its complex distribution. As an alternative, this paper proposes the best linear procedure and verifies its effectiveness. For this, the present paper provides the necessary theories for deriving the linear rule and its properties, an efficient inference, and a simulation study that sheds light on the performance of the best linear procedure. It also provides three real data examples to demonstrate the applicability of the best linear procedure.