On a balanced quadratic classification rule

Abstract

Quadratic classification rule is considered in the case when the prior probability of an individual belonging to one of the two multivariate normal populations is unknown. An alternative to the usual quadratic classification rule which uses little knowledge estimate of the prior probability is proposed in a closed form. The alternative is characterized by a constrained minimization of the total risk of misclassification, the constraint of which is constructed by the process of equation between the expected utilities of the population distributions suggested by Bernardo(1979). The efficacy of the suggested rule is examined through simulation studies. This indicates that in many circumstances dramatic gains in classification accuracy can be achieved.

Keywords:

• Quadratic classification rule
• prior probability
• balanced design
• total probability of misclassification
• constrained minimization