F. Liese, K.J. Miescke
Exponential Rates for the Error Probabilities in Selection Procedures
Preprint series: Preprints aus dem Fachbereich Mathematik, Universität Rostock

MSC:

62F07 Ranking and selection

62F35 Robustness and adaptive procedures

Abstract: For a sequence of statistical experiments with a finite
parameter set the asymptotic behavior of the maximum risk is
studied for the problem of classification into disjoint subsets.
The exponential rates of the optimal decision rule is determined
and expressed in terms of the normalized limit of moment
generating functions of likelihood ratios. Necessary and
sufficient conditions for the existence of adaptive
classification rules in the sense of Rukhin [10] are given. The
results are applied to the problem of the selecting of the best
population. Exponential families are studied as a special case,
and an example for the normal case is included.
Keywords: Adaptive classifications and selections, asymptotic error probabilities, exponential families