Ein kombiniertes test & klassifikations-problem |
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Authors: | Dozent Dr Johann Pfanzagl |
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Institution: | 1. Institut für Statistik an der Universit?t Wien, Austria
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Abstract: | Summary A decision process is considered which consists of two steps: First, a nullhypothesis H0 is to be tested. If H0 is rejected, a decision is to be made as to which of the alternative hypotheses H1, H2, ... H
k
is valid. This second step is called "classification". It is assumed, that in case H0 is not valid, each of the alternative hypotheses H1, H2, ... H
k
has the same probability. Starting with this assumption, an optimal decision process is developed which has a specified level
of significance α (i.e. by which the nullhypothesis H0 is accepted with probability α, if it is valid), and for which the probability of a correct classification is a maximum in
the case where the nullhypothesis is not valid. This decision process rests on a generalisation of the fundamental lemma of
Neyman and Pearson, similar to that used in discriminant analysis. |
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Keywords: | |
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