Martín Apaolaza, NíriamPardo Llorente, Leandro2023-06-202023-06-2020110233-188810.1080/02331888.2010.485275https://hdl.handle.net/20.500.14352/42424For some discrete state series, such as DNA sequences, it can often be postulated that its probabilistic behaviour is given by a Markov chain. For making the decision on whether or not an uncharacterized piece of DNA is part of the coding region of a gene, under the Markovian assumption, there are two statistical tools that are essential to be considered: the hypothesis testing of the order in a Markov chain and the estimators of transition probabilities. In order to improve the traditional statistical procedures for both of them when stationarity assumption can be considered, a new version for understanding the homogeneity hypothesis is proposed so that log-linear modelling is applied for conditional independence jointly with homogeneity restrictions on the expected means of transition counts in the sequence. In addition we can consider a variety of test-statistics and estimators by using phi-divergence measures. As special case of them the well-known likelihood ratio test-statistics and maximum-likelihood estimators are obtained.engjournal articlehttp://www.tandfonline.com/doi/pdf/10.1080/02331888.2010.485275http://www.tandfonline.com/restricted access519.234contingency tablelog-linear modelrestricted estimatorconditional test statisticMaximum-likelihood methodsEstadística matemática (Matemáticas)1209 Estadística