Maximum Likelihood Estimation by Monte Carlo Simulation: Toward Data-Driven Stochastic Modeling

• 成果类型: Article
• 署名作者: Peng, Yijie; Fu, Michael C.; Heidergott, Bernd; Lam, Henry
• 署名单位: Peking University; University System of Maryland; University of Maryland College Park; University System of Maryland; University of Maryland College Park; Vrije Universiteit Amsterdam; Columbia University
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2019.1978
• 发表日期: 2020
• 页码: 1896-1912
• 关键词: simulation; sensitivity analysis; generalized likelihood ratio method; gradient-based MLE

摘要

We propose a gradient-based simulated maximum likelihood estimation to estimate unknown parameters in a stochastic model without assuming that the likelihood function of the observations is available in closed form. A key element is to develop Monte Carlo-based estimators for the density and its derivatives for the output process, using only knowledge about the dynamics of the model. We present the theory of these estimators and demonstrate how our approach can handle various types of model structures. We also support our findings and illustrate the merits of our approach with numerical results.