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A Note on Consistent Estimation of Multivariate Parameters in Ergodic Diffusion Models

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  • J. H. Van Zanten

Abstract

Certain aspects of maximum likelihood estimation for ergodic diffusions are studied via recently developed empirical process theory for martingales. This approach enables us to remove some undesirable regularity conditions that usually appear in the statistical literature on ergodic diffusions. In particular, dimension dependent conditions for the existence of a continuous likelihood and for consistency of the maximum likelihood estimator turn out to be unnecessary.

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  • J. H. Van Zanten, 2001. "A Note on Consistent Estimation of Multivariate Parameters in Ergodic Diffusion Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(4), pages 617-623, December.
    • Handle: RePEc:bla:scjsta:v:28:y:2001:i:4:p:617-623
    DOI: 10.1111/1467-9469.00258
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    Cited by:

    1. Jaromir Sant & Paul A. Jenkins & Jere Koskela & Dario Spanò, 2022. "Convergence of likelihood ratios and estimators for selection in nonneutral Wright–Fisher diffusions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(4), pages 1728-1760, December.
    2. Papavasiliou, A. & Pavliotis, G.A. & Stuart, A.M., 2009. "Maximum likelihood drift estimation for multiscale diffusions," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3173-3210, October.
    3. Loukianova, D. & Loukianov, O., 2005. "Uniform law of large numbers and consistency of estimators for Harris diffusions," Statistics & Probability Letters, Elsevier, vol. 74(4), pages 347-355, October.

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