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Asymptotic Expansions for Perturbed Systems on Wiener Space: Maximum Likelihood Estimators

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  • Yoshida, Nakahiro
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    Abstract

    By means of the Malliavin Calculus, we derive asymptotic expansion of the probability distributions of statistics for systems perturbed by small noises. These results are applied to the problem of the second order asymptotic efficiency of the maximum likelihood estimator.

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    File URL: http://www.sciencedirect.com/science/article/B6WK9-45NJFJT-T/2/638711fde5d95be70f052fb38f800e7c
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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 57 (1996)
    Issue (Month): 1 (April)
    Pages: 1-36

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    Handle: RePEc:eee:jmvana:v:57:y:1996:i:1:p:1-36

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    Related research

    Keywords: maximum likelihood estimator Malliavin calculus asymptotic expansion (null);

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    Cited by:
    1. Tomonari Sei & Fumiyasu Komaki, 2008. "Information geometry of small diffusions," Statistical Inference for Stochastic Processes, Springer, vol. 11(2), pages 123-141, June.
    2. Akihiko Takahashi & Kohta Takehara & Masashi Toda, 2009. "Computation in an Asymptotic Expansion Method," CIRJE F-Series CIRJE-F-621, CIRJE, Faculty of Economics, University of Tokyo.
    3. Masayuki Uchida & Nakahiro Yoshida, 2004. "Asymptotic Expansion for Small Diffusions Applied to Option Pricing," Statistical Inference for Stochastic Processes, Springer, vol. 7(3), pages 189-223, October.
    4. Yoshida, Nakahiro, 2003. "Conditional expansions and their applications," Stochastic Processes and their Applications, Elsevier, vol. 107(1), pages 53-81, September.
    5. Yuji Sakamoto & Nakahiro Yoshida, 2004. "Asymptotic expansion formulas for functionals of ε-Markov processes with a mixing property," Annals of the Institute of Statistical Mathematics, Springer, vol. 56(3), pages 545-597, September.
    6. Masayuki Uchida & Nakahiro Yoshida, 2004. "Information Criteria for Small Diffusions via the Theory of Malliavin–Watanabe," Statistical Inference for Stochastic Processes, Springer, vol. 7(1), pages 35-67, March.

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