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Parametric estimation for partially hidden diffusion processes sampled at discrete times


  • Iacus, Stefano Maria
  • Uchida, Masayuki
  • Yoshida, Nakahiro


For a one-dimensional diffusion process , we suppose that X(t) is hidden if it is below some fixed and known threshold [tau], but otherwise it is visible. This means a partially hidden diffusion process. The problem treated in this paper is the estimation of a finite-dimensional parameter in both drift and diffusion coefficients under a partially hidden diffusion process obtained by a discrete sampling scheme. It is assumed that the sampling occurs at regularly spaced time intervals of length hn such that nhn=T. The asymptotic is when hn-->0, T-->[infinity] and as n-->[infinity]. Consistency and asymptotic normality for estimators of parameters in both drift and diffusion coefficients are proved.

Suggested Citation

  • Iacus, Stefano Maria & Uchida, Masayuki & Yoshida, Nakahiro, 2009. "Parametric estimation for partially hidden diffusion processes sampled at discrete times," Stochastic Processes and their Applications, Elsevier, vol. 119(5), pages 1580-1600, May.
  • Handle: RePEc:eee:spapps:v:119:y:2009:i:5:p:1580-1600

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    References listed on IDEAS

    1. Yoshida, Nakahiro, 1992. "Estimation for diffusion processes from discrete observation," Journal of Multivariate Analysis, Elsevier, vol. 41(2), pages 220-242, May.
    2. Paul Fearnhead & Omiros Papaspiliopoulos & Gareth O. Roberts, 2008. "Particle filters for partially observed diffusions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(4), pages 755-777.
    3. Nakahiro Yoshida, 1990. "Asymptotic behavior of M-estimator and related random field for diffusion process," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 42(2), pages 221-251, June.
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    Cited by:

    1. repec:spr:sistpr:v:20:y:2017:i:2:d:10.1007_s11203-016-9142-4 is not listed on IDEAS
    2. Yoshida, Nakahiro, 2013. "Martingale expansion in mixed normal limit," Stochastic Processes and their Applications, Elsevier, vol. 123(3), pages 887-933.


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