caa a22 4500 378875442 CHVBK 20180305123419.0 cr unu---uuuuu 161128e20030701xx s 000 0 eng 10.1515/156939203322385928 doi (NATIONALLICENCE)gruyter-10.1515/156939203322385928 On two statistics of chi-square type based on frequencies of tuples of states of a high-order Markov chain [Elektronische Daten] [M. I. Tikhomirova, V. P. Chistyakov] We consider a tuple of states of an (s - 1)-order Markov chain whose transition probabilities depend on a small part of s - 1 preceding states. We obtain limit distributions of certain χ2-statistics X and Y based on frequencies of tuples of states of the Markov chain. For the statistic X, frequencies of tuples of only those states are used on which the transition probabilities depend, and for the statistic Y, frequencies of s-tuples without gaps. The statistical test with statistic X which distinguishes the hypotheses H 1 (a high-order Markov chain) and H 0 (an independent equiprobable sequence) appears to be more powerful than the test with statistic Y . The statistic Z of the Neyman-Pearson test, as well as X, depends only on frequencies of tuples with gaps. The statistics X and Y are calculated without use of distribution parameters under the hypothesis H 1, and their probabilities of errors of the first and second kinds depend only on the non-centrality parameter, which is a function of transition probabilities. Thus, for these statistics the hypothesis H 1 can be considered as composite. Copyright 2003, Walter de Gruyter Tikhomirova M. I. aut Chistyakov V. P. aut Discrete Mathematics and Applications Walter de Gruyter 13/3(2003-07-01), 319-329 0924-9265 13:3<319 2003 13 dma https://doi.org/10.1515/156939203322385928 text/html Onlinezugriff via DOI 1 research article jats NATIONALLICENCE 856 40 https://doi.org/10.1515/156939203322385928 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Tikhomirova M. I. aut NATIONALLICENCE 700 1- Chistyakov V. P. aut NATIONALLICENCE 773 0- Discrete Mathematics and Applications Walter de Gruyter 13/3(2003-07-01), 319-329 0924-9265 13:3<319 2003 13 dma CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-gruyter