Adaptive Classification Procedures
Andrew L. Rukhin · Journal of the American Statistical Association · 1984
An explicitly computable, necessary, and sufficient condition for the existence of an adaptive classification procedure is obtained. By definition, an adaptive procedure, which classifies a sample as coming from one of alternative distributions known only up to a finite-valued nuisance parameter, is required to have the same asymptotic behavior of error probability for these families as asymptotically optimal rules for each of the families. We investigate the conditions under which the overall maximum likelihood procedure is adaptive and derive a rule that is adaptive if any procedure is. We study the consistency of these procedures. Several exponential-family examples illustrate their form, and a small-sample study of error probabilities is performed.