Fitting DNA sequences through log-linear modelling with linear constraints. (English) Zbl 1228.62144
Summary: For 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 the 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.
MSC:
| 62P10 | Applications of statistics to biology and medical sciences; meta analysis |
| 62M02 | Markov processes: hypothesis testing |
| 62H17 | Contingency tables |
| 92C40 | Biochemistry, molecular biology |
| 62M05 | Markov processes: estimation; hidden Markov models |
| 62B10 | Statistical aspects of information-theoretic topics |
| 65C60 | Computational problems in statistics (MSC2010) |
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