Adaptive Classification Procedures
本文给出了自适应分类程序存在的可计算充要条件，研究了最大似然方法的自适应性，并通过指数族例子和小样本误差概率分析验证了其形式与一致性。
Abstract 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.