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A quasi-likelihood approach to estimating parameters in diffusion-type processes

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

C. C. Heyde
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Abstract

Estimation of parameters in diffusion models is usually handled by maximum likelihood and involves the calculation of a Radon–Nikodym derivative. This methodology is often not available when minor changes are made to the model. However, these complications can usually be avoided and results obtained under more general conditions using quasi-likelihood methods. The basic ideas are explained in this paper and are illustrated through discussion of the Cox–Ingersoll–Ross model and a modification of the Langevin model.

Keywords

COX-INGERSOLL-ROSS MODELLANGEVIN MODELINFERENCEPARAMETER ESTIMATIONDIFFUSION PROCESSES

MSC classification

Primary: 60J60: Diffusion processes
Type
Part 5 Statistical Studies
Information
Journal of Applied Probability , Volume 31 , Issue A , 1994 , pp. 283 - 290
Copyright
Copyright © Applied Probability Trust 1994 

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References

Basawa, I. V. and Prakasa Rao, B. L. S. (1980) Statistical Inference for Stochastic Processes. Academic Press, London.Google Scholar
Cox, J. S., Ingersoll, J. E. and Ross, S. A. (1985) A theory of the term structure of interest rates. Econometrica 53, 363–384.Google Scholar
Godambe, V. P. (1960) An optimum property of regular maximum likelihood estimation. Ann. Math. Statist. 31, 1208–1211.CrossRefGoogle Scholar
Godambe, V. P. and Heyde, C. C. (1987) Quasi-likelihood and optimal estimation. Int. Statist. Rev. 55, 231–244.CrossRefGoogle Scholar
Heyde, C. C. (1988) Fixed sample and asymptotic optimality for classes of estimating functions. Contemp. Math. 80, 241–247.CrossRefGoogle Scholar
Heyde, C. C. (1989) Quasi-likelihood and optimality for estimating functions: some current unifying themes. Bull. Int. Statist. Inst. 53(1), 19–29.Google Scholar
Kloeden, P. E. and Platen, E. (1992) Numerical Solution of Stochastic Differential Equations. Springer-Verlag, Berlin.Google Scholar
Lin, Y.-X. and Heyde, C. C. (1993) Optimal estimating functions and Wedderburn's quasi-likelihood. Commun. Statist. Theory Meth. 22, 2341–2350.Google Scholar
Lipster, R. S. and Shiryaev, A. N. (1977) Statistics of Random Processes I. General Theory. Springer-Verlag, New York.Google Scholar
Mccullagh, P. and Nelder, J. A. (1989) Generalized Linear Models , 2nd edn. Chapman and Hall, London.Google Scholar
Rogers, L. C. G. and Williams, D. (1987) Diffusions, Markov Processes and Martingales. Vol. 2 Ito Calculus. Wiley, Chichester.Google Scholar
Sørensen, M. (1990) On quasi-likelihood for semimartingales. Stoch. Proc. Appl. 25, 331–346.Google Scholar
Wedderburn, R. W. M. (1974) Quasi-likelihood functions, generalized linear models, and the Gauss-Newton method. Biometrika 61, 439–447.Google Scholar