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Globally optimal parameter estimates for nonlinear diffusions
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Mijatović, Aleksandar and Schneider, Paul (2010) Globally optimal parameter estimates for nonlinear diffusions. Annals of statistics, Vol.38 (No.1). pp. 215-245. doi:10.1214/09-AOS710 ISSN 0090-5364.
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Official URL: http://dx.doi.org/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 its closed-form likelihood expansions.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Social Sciences > Warwick Business School | ||||
Library of Congress Subject Headings (LCSH): | Diffusion processes | ||||
Journal or Publication Title: | Annals of statistics | ||||
Publisher: | Inst Mathematical Statistics | ||||
ISSN: | 0090-5364 | ||||
Official Date: | February 2010 | ||||
Dates: |
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Volume: | Vol.38 | ||||
Number: | No.1 | ||||
Number of Pages: | 31 | ||||
Page Range: | pp. 215-245 | ||||
DOI: | 10.1214/09-AOS710 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Open Access (Creative Commons) | ||||
Date of first compliant deposit: | 8 December 2015 | ||||
Date of first compliant Open Access: | 8 December 2015 |
Data sourced from Thomson Reuters' Web of Knowledge
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