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Likelihood and quasi - likelihood estimation of transition probabilities
Discussiones Mathematicae. Probability and Statistics, Tome 24 (2004) no. 1, pp. 77-84 Cet article a éte moissonné depuis la source Library of Science

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In the paper two approaches to the problem of estimation of transition probabilities are considered. The approach by McCullagh and Nelder [5], based on the independent model and the quasi-likelihood function, is compared with the approach based on the marginal model and the standard likelihood function. The estimates following from these two approaches are illustrated on a simple example which was used by McCullagh and Nelder.
Keywords: likelihood estimation, quasi-likelihood estimation, transition probabilities, quasi-information matrix 
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Bakinowska, Ewa; Kala, Radosław. Likelihood and quasi - likelihood estimation of transition probabilities. Discussiones Mathematicae. Probability and Statistics, Tome 24 (2004) no. 1, pp. 77-84. http://geodesic.mathdoc.fr/item/DMPS_2004_24_1_a3/

[1] D.L. Hawkins and C.-P. Han, Estimating Transition Probabilities from Aggregate Samples Plus Partial Transition Data, Biometrics 56 (2000), 848-854.

[2] J.D. Kalbfleisch, J.F. Lawless and W.M. Vollomer, Estimation in Markov Models from Aggregate Data, Biometrics 39 (1983), 907-919.

[3] T.C. Lee, G.G. Judge and A. Zellender, Estimating the Parameters of the Markov Probability Model from Aggregate Time Series Data, New York, North Holland 1977.

[4] P. McCullagh and J.A. Nelder, Generalized Linear Models, Chapman and Hall, London 1983.

[5] P. McCullagh and J.A. Nelder, Generalized Linear Models, 2nd. ed. Chapman and Hall, London 1989.

[6] R.W.M. Wedderburn, Quasi-likelihood Functions, Generalized Linear Models, and the Gauss-Newton method, Biometrika Wedderburn, 61 (1974), 439-447.