Discrimination models on two probability distributions
M. P. Gessaman · Montana State University ScholarWorks (Montana State University) · 1966
The discrimination problem for two probability distributions can be briefly described as follows: an individual is observed at random from a collection known to consist of elements from two distinct populations, and this individual is to be classified as to its parent population.A discrimination model is constructed which requires control of the probability of misclassification under each distribution.In order to do this, a point must be included in the decision space which allows for reserving judgment, i.e. making no classification.The power for discrimination is defined as the overall probability that a decision is made.If the level is chosen by the investigator, then the discrimination problem is the search for a discrimination procedure, if it exists, which is most powerful for discrimination at the chosen level. When both distributions are completely known, a solution under quite general hypotheses is found.A nonparametric discrimination model is given and a method for constructing procedures approximately of the required size is outlined.The theory of coverages is used in this construction.A consistency for sequences of discrimination procedures is defined.Under restricted models, sequences of discrimination procedures based on the theory of coverages are found which are consistent with an optimal procedure.When consistency does not seem possible, procedures which have some appeal are suggested.