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On estimation in the planar Ornstein-Uhlenbeck process. (English) Zbl 0891.62059

Summary: Three types of estimators based on data sampled from a complete rectangular lattice of points are studied. The least squares (LS), the optimal estimating function (OEF) and maximum likelihood (ML) estimators are compared for large samples of data generated by a Gaussian two variable Ornstein-Uhlenbeck process. It is shown that for a constant lag spacing the three estimators have the same asymptotic normal distribution as the sample size is growing, while if we fix the area of sampling and increase the sample size by refining partition of the area, the ML estimator has asymptotically smaller variance than the LS and OEF estimators. Behavior of the estimators is demonstrated on measured and simulated data.

MSC:

62M05 Markov processes: estimation; hidden Markov models
62F12 Asymptotic properties of parametric estimators
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