Discussiones Mathematicae Probability and Statistics 24(1) (2004) 77-84

LIKELIHOOD AND QUASI-LIKELIHOOD ESTIMATION OF TRANSITION PROBABILITIES

Ewa Bakinowska and Radosław Kala

Department of Mathematical and Statistical Methods
Agricultural University of Poznań
Wojska Polskiego 28, PL 60637 Poznań, Poland

Abstract

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.

2000 Mathematics Subject Classification: 62F10, 62F05.

References

[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.

Received 4 October 2003