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Uniform law of large numbers and consistency of estimators for Harris diffusions

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  • Loukianova, D.
  • Loukianov, O.

Abstract

Consider a family of local martingales depending on a parameter [theta] running through some compact in . We show that if their quadratic variations are Hölder in [theta], then the family satisfies a uniform law of large numbers. We apply it to deduce the almost sure consistency of maximum likelihood estimators for drift parameters of a multidimensional Harris recurrent diffusion, thereby extending a recent result of J.H. van Zanten for one-dimensional ergodic diffusions.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:74:y:2005:i:4:p:347-355
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    References listed on IDEAS

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    1. Harry Van Zanten, 2003. "On Uniform Laws of Large Numbers for Ergodic Diffusions and Consistency of Estimators," Statistical Inference for Stochastic Processes, Springer, vol. 6(2), pages 199-213, May.
    2. Jankunas, Andrius & Khasminskii, Rafail Z., 1997. "Estimation of parameters of linear homogeneous stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 72(2), pages 205-219, December.
    3. R. Höpfner & Yu. Kutoyants, 2003. "On a Problem of Statistical Inference in Null Recurrent Diffusions," Statistical Inference for Stochastic Processes, Springer, vol. 6(1), pages 25-42, January.
    4. Senoussi, R., 2000. "Uniform iterated logarithm laws for martingales and their application to functional estimation in controlled Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 89(2), pages 193-211, October.
    5. 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.
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