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February 2010 Globally optimal parameter estimates for nonlinear diffusions
Aleksandar Mijatović, Paul Schneider
Ann. Statist. 38(1): 215-245 (February 2010). DOI: 10.1214/09-AOS710

Abstract

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 1) 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.

Citation

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Aleksandar Mijatović. Paul Schneider. "Globally optimal parameter estimates for nonlinear diffusions." Ann. Statist. 38 (1) 215 - 245, February 2010. https://doi.org/10.1214/09-AOS710

Information

Published: February 2010
First available in Project Euclid: 31 December 2009

zbMATH: 1181.62121
MathSciNet: MR2589321
Digital Object Identifier: 10.1214/09-AOS710

Subjects:
Primary: 60J60 , 62F12

Keywords: EM algorithm , estimation , global optimization , maximum likelihood , Nonlinear diffusion

Rights: Copyright © 2010 Institute of Mathematical Statistics

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Vol.38 • No. 1 • February 2010
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