G1-minimax procedures for the case of prior distributions in discriminant analysis

Abstract

In discriminant analysis, let q ′ = ( q 1 , …, q m ) denote the vector of prior probabilities associated with an observation coming from populations II 1 , …, II m , respectively. Present approaches either consider q fixed and known, and use the corresponding Bayes procedure, or, if q is unknown, assume that the q i are equal, and use the Bayes procedure based on that assumption. In this paper, consideration is given to the idea of a prior distribution on q , and procedures are developed which are optimal for the class G 1 , of all priors on q with specified first moment. In addition, a procedure is suggested which would incorporate an estimate of the prior mean into the discrimination procsedure.