Globally optimal parameter estimates for nonlinear diffusions

Details Globally optimal parameter estimates for nonlinear diffusions Globally optimal parameter estimates for nonlinear diffusions

2009-05-20

arxiv.org/abs/0905.3321v2

Annals of Statistics 2010, Vol. 38, No. 1, 215-245

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/09-AOS710 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of

Scientific paper

10.1214/09-AOS710

This paper studies an approximation method for the log-likelihood function of a nonlinear diffusion process using the bridge of the diffusion. The main result (Theorem \refthm:approx) shows that this approximation converges uniformly to the unknown likelihood function and can therefore be used efficiently with any algorithm for sampling from the law of the bridge. We also introduce an expected maximum likelihood (EML) algorithm for inferring the parameters of discretely observed diffusion processes. The approach is applicable to a subclass of nonlinear SDEs with constant volatility and drift that is linear in the model parameters. In this setting, globally optimal parameters are obtained in a single step by solving a linear system. Simulation studies to test the EML algorithm show that it performs well when compared with algorithms based on the exact maximum likelihood as well as closed-form likelihood expansions.

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