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Quasi-likelihood estimation for semimartingales. (English) Zbl 0616.62113
The paper proposes a new technique of parameter estimation for a class of semimartingales, continuous in time, based on a certain type of quasi- likelihood. The class of semi-martingales contains many widely used continuous time stochastic models (e.g. diffusions, Poisson processes and branching processes). The quasi-likelihood to be maximized can be understood as a generalization of the quasi-likelihood introduced by R. W. M. Wedderburn [Biometrika 61, 439-447 (1974; Zbl 0292.62050)] in the context of generalized linear models. Consistency and asymptotic normality of the estimator, as well as optimality in the sense of V. P. Godambe [see Ann. Math. Stat. 31, 1208-1211 (1960; Zbl 0118.343)], are shown under assumptions which do not rule out nonstationary or non- Markovian behaviour of the process.
Reviewer: L.Fahrmeier

MSC:
62M09 Non-Markovian processes: estimation
62F12 Asymptotic properties of parametric estimators
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