Adaptive tests and classification procedures
Abstract
The problems of hypotheses testing and classification are considered when the distribution of a random sample is specified only up to a nuisance parameter. An adaptive procedure is defined to be one which is asymptotically optimal regardless of the value of the nuisance parameter. In the cases of hypotheses testing, two asymptotic optimality criteria are considered: (1) the rates of convergence of the probability of type I and type II errors, (2) the rate of convergence of the level attained by the test statistic. In the classification problem we consider procedures which minimize asymptotically the maximum probability of misclassification. In both cases, necessary and sufficient conditions for the existence of adaptive procedures are obtained. Also, adaptive procedures are constructed when they exist.
Degree
Ph.D.
Advisors
Rukhin, Purdue University.
Subject Area
Statistics
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