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

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  • Yoshida, Nakahiro

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.

Suggested Citation

  • Yoshida, Nakahiro, 1996. "Asymptotic Expansions for Perturbed Systems on Wiener Space: Maximum Likelihood Estimators," Journal of Multivariate Analysis, Elsevier, vol. 57(1), pages 1-36, April.
    • Handle: RePEc:eee:jmvana:v:57:y:1996:i:1:p:1-36
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    Citations

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    Cited by:

    1. 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.
    2. Yoshida, Nakahiro, 2023. "Asymptotic expansion and estimates of Wiener functionals," Stochastic Processes and their Applications, Elsevier, vol. 157(C), pages 176-248.
    3. Tudor, Ciprian A. & Yoshida, Nakahiro, 2023. "High order asymptotic expansion for Wiener functionals," Stochastic Processes and their Applications, Elsevier, vol. 164(C), pages 443-492.
    4. 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;The Institute of Statistical Mathematics, vol. 56(3), pages 545-597, September.
    5. Tomonari Sei & Fumiyasu Komaki, 2008. "Information geometry of small diffusions," Statistical Inference for Stochastic Processes, Springer, vol. 11(2), pages 123-141, June.
    6. 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.
    7. Yoshida, Nakahiro, 2003. "Conditional expansions and their applications," Stochastic Processes and their Applications, Elsevier, vol. 107(1), pages 53-81, September.
    8. 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.
    9. Akihiko Takahashi & Kohta Takehara & Masashi Toda, 2009. "Computation in an Asymptotic Expansion Method," CARF F-Series CARF-F-149, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.

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