The Annals of Statistics

Monte Carlo maximum likelihood estimation for discretely observed diffusion processes

Alexandros Beskos, Omiros Papaspiliopoulos, and Gareth Roberts

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This 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→∞, 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.

Article information

Ann. Statist. Volume 37, Number 1 (2009), 223-245.

First available in Project Euclid: 16 January 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 65C30: Stochastic differential and integral equations
Secondary: 62M05: Markov processes: estimation

Coupling uniform convergence exact simulation linear diffusion processes random function SLLN on Banach space


Beskos, Alexandros; Papaspiliopoulos, Omiros; Roberts, Gareth. Monte Carlo maximum likelihood estimation for discretely observed diffusion processes. Ann. Statist. 37 (2009), no. 1, 223--245. doi:10.1214/07-AOS550.

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