A decision theoretic approach to a distribution–free compound classification problem

Abstract

A compound decision problem with component decision problem being the classification of a random sample as having come from one of the finite number of univariate populations is investigated. The Bayesian approach is discussed. A distribution–free decision rule is presented which has asymptotic risk equal to zero. The asymptotic efficiencies of these rules are discussed.

The results of a compter simulation are presented which compares the Bayes rule to the distribution–free rule under the assumption of normality. It is found that the distribution–free rule can be recommended in situations where certain key lo cation parameters are not known precisely and/or when certain distributional assumptions are not satisfied.

Keywords:

• Classification
• Bayesian
• nonparametric rules