Monte Carlo maximum likelihood estimation for discretely observed diffusion processes

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dc.creatorBeskos, Alexandros
dc.creatorPapaspiliopoulos, Omiros
dc.creatorRoberts, Gareth
dc.date2009-03-02
dc.date.accessioned2026-07-07T12:48:10Z
dc.date.available2026-07-07T12:48:10Z
dc.descriptionThis paper introduces a Monte Carlo method for maximum likelihood inference in the context of discretely observed diffusion processes. The method gives unbiased and a.s.\@ continuous estimators of the likelihood function for a family of diffusion models and its performance in numerical examples is computationally efficient. It uses a recently developed technique for the exact simulation of diffusions, and involves no discretization error. We show that, under regularity conditions, the Monte Carlo MLE converges a.s. to the true MLE. For datasize $n\to\infty$, we show that the number of Monte Carlo iterations should be tuned as $\mathcal{O}(n^{1/2})$ and we demonstrate the consistency properties of the Monte Carlo MLE as an estimator of the true parameter value.
dc.descriptionPublished in at http://dx.doi.org/10.1214/07-AOS550 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/0903.0290
dc.identifierhttp://arxiv.org/abs/0903.0290
dc.identifierAnnals of Statistics 2009, Vol. 37, No. 1, 223-245
dc.identifierdoi:10.1214/07-AOS550
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/221962
dc.subjectStatistics Theory
dc.subject65C30 (Primary) 62M05 (Secondary)
dc.titleMonte Carlo maximum likelihood estimation for discretely observed diffusion processes
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