Abstract: This paper is devoted to study of characteristics of logarithmically asymptotically optimal (LAO) hypotheses testing and identification for a model consisting of two related objects. In general case it is supposed that L1 possible probability distributions of states constitute the family of possible hypotheses for the first object and the second object is distributed according to one of L1 × L2 given conditional distributions depending on the distribution index and the current observed state of the first object. For the first testing procedure the matrix of interdependencies of all possible pairs of the error probability exponents (reliabilities) in asymptotically optimal tests of distributions of both objects is studied. The identification of the distributions of two objects gives an answer to the question whether 1 r -th and 2r -th distributions occurred or not on the first and the second objects, correspondingly. Reliabilities for the LAO identification are determined for each pair of double hypotheses. By the second approach the optimal interdependencies of lower estimates of all possible pairs of corresponding reliabilities are found and lower estimates of reliabilities for the LAO identification are studied for each pair of hypotheses. The more complete results are presented for model of statistically dependent objects, when distributions of the objects are dependent, but its current states are independent. For an example of two statistically dependent objects optimal interdependencies of pairs of reliabilities are calculated and graphically presented.

Keywords: Multiple hypotheses testing, Identification of distribution, Inference of many objects, Error probability exponents, Reliabilities.

Link:

ON RELIABILITY APPROACH TO MULTIPLE HYPOTHESES TESTING AND TO IDENTIFICATION OF PROBABILITY DISTRIBUTIONS OF TWO STOCHASTICALLY RELATED OBJECTS

Evgueni Haroutunian, Aram Yessayan, Parandzem Hakobyan

http://www.foibg.com/ijita/vol17/ijita17-3-p06.pdf