Multiple hypotheses optimal testing with rejection option for many objects

Haroutunian Evgueni

Multiple hypotheses optimal testing with rejection option for many objects

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Title: Multiple hypotheses optimal testing with rejection option for many objects

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The multiple statistical hypotheses testing with possibility of rejecting of decision for discrete independent observations is investigated for models consisting of two independent objects. The matrix of optimal asymptotical interdependencies of possible pairs of the error probability exponents (reliabilities) is studied. For an asymptotically optimal test the probability of error decreases exponentially when the number of observations tends to infinity. Such tests were profoundly studied for case of two hypotheses by many authors. The sequence of such tests was called logarithmically asymptotically optimal (LAO). Haroutunian [1, 2] investigated the problem of LAO testing for multiple hypotheses. In publications [3]– [5] many hypotheses LAO testing for the model consisting of many independent objects was studied. The multiple hypotheses testing problem with possibility of rejection of decision for arbitrarily varying object with side information was examined in [6] and [7]. This report is devoted to study of characteristics of logarithmically asymptotically optimal (LAO) hypotheses testing with possibility of rejection of decision for the model consisting of two independent objects. In the report two models are studied, the first when the rejection of decision is allowed to one of the objects and the second when the rejection of decision is allowed to both objects. The study is based on information theoretic methods. Applications of information theory in mathematical statistics, specifically in hypotheses testing, are exposed in multiple works and also in the monographs by Cover and Thomas [8], Csisz´ar and Shields [9], Csisz´ar and K¨orner [10], Blahut [11].