Menéndez Calleja, María LuisaPardo Llorente, Julio ÁngelPardo Llorente, Leandro2023-06-202023-06-202001-070932-5026http://dx.doi.or/10.1007/s003620100061https://hdl.handle.net/20.500.14352/57781Assume that a sequence of observations x(1),...,x(n+r) can be treated as the sample values of a Markov chain of order r or less (chain in which the dependence extends over r+1 consecutive variables only), and consider the problem of testing the hypothesis No that a chain of order r - 1 will be sufficient on the basis of the tools given by the Statistical Information Theory: rho -Divergences. More precisely, if p(a1),...,(ar:ar+1) denotes the transition probability for a r(th) order Markov chain, the hypothesis to be tested is H-0 : p(a1),...,(ar:ar+1) = p(a2),...,(ar):(ar+1), a(i) is an element of {1,...,s}, i = 1,..., r + 1 The tests given in this paper, for the first time, will have as a particular case the likelihood ratio test and the test based on the chi-squared statistic.engjournal articlehttp://www.springerlink.com/content/wtr4a6q9bqftaq6w/fulltext.pdfhttp://www.springerlink.comrestricted access519.216r th Markov chainsCsiszar's phi-divergencesStatistical Information Theorygoodness of fit testsdivergence statistics.Probabilidades (Matemáticas)