Application of LDT to Many Hypotheses Optimal Testing for Markov Chain
Abstract
The problem of many (L > 2) hypotheses testing on distributions of a finite state Markov chain is studied. We apply large deviations techniques (LDT). It is proved that this method of investigation in solving the problem of logarithmically asymptotically optimal (LAO) hypotheses testing is easier than the procedure that was introduced by Haroutunian. The matrix of exponents E = fEljmg; m; l = 1;L, of error probabilities of the LAO test Eljm(Á) = lim N!1¡ 1 N log ®ljm(ÁN); where ®Nl jm(ÁN) for l 6= m is the probability to accept the hypothesis l, when the hypothesis m is true, is determined.
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