Parametric estimation for partially hidden diffusion processes sampled at discrete times
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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Volume (Year): 119 (2009)
Issue (Month): 5 (May)
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- 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.
- Yoshida, Nakahiro, 1992. "Estimation for diffusion processes from discrete observation," Journal of Multivariate Analysis, Elsevier, vol. 41(2), pages 220-242, May.
- 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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