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Parametric estimation for partially hidden diffusion processes sampled at discrete times

Listed author(s):
  • 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.

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File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(08)00126-9
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Article provided by Elsevier in its journal Stochastic Processes and their Applications.

Volume (Year): 119 (2009)
Issue (Month): 5 (May)
Pages: 1580-1600

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Handle: RePEc:eee:spapps:v:119:y:2009:i:5:p:1580-1600
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  1. 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.
  2. Yoshida, Nakahiro, 1992. "Estimation for diffusion processes from discrete observation," Journal of Multivariate Analysis, Elsevier, vol. 41(2), pages 220-242, May.
  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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