GLOBALLY OPTIMAL PARAMETER ESTIMATES FOR NONLINEAR DIFFUSIONS

• 成果类型: Article
• 署名作者: Mijatovic, Aleksandar; Schneider, Paul
• 署名单位: Imperial College London; University of Warwick
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/09-AOS710
• 发表日期: 2010
• 页码: 215-245
• 关键词: maximum-likelihood-estimation; stochastic differential-equations; closed-form approximation; simulated likelihood; Numerical techniques; models; time; inference; volatility; algorithm

摘要

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.