Parameter Estimation of Nonlinear Stochastic Differential Equations: Simulated Maximum Likelihood versus Extended Kalman Filter and Itô-Taylor Expansion
比较了模拟极大似然法、扩展卡尔曼滤波等几种估计非线性随机微分方程参数的方法，通过双阱势扩散和广义Cox-Ingersoll-Ross模型模拟发现，大采样间隔时模拟极大似然法更优，而扩展卡尔曼滤波在特定情况下是高效替代方案。
This article compares several estimation methods for nonlinear stochastic differential equations with discrete time measurements. The likelihood function is computed by Monte Carlo simulations of the transition probability (simulated maximum likelihood SML) using kernel density estimators and functional integrals and by using the extended Kalman filter (EKF and second-order nonlinear filter SNF). The relation with a local linearization method is discussed. A simulation study for a diffusion process in a double well potential (Ginzburg–Landau equation) shows that, for large sampling intervals, the SML methods lead to better estimation results than the likelihood approach via EKF and SNF. A second study using a nonlinear diffusion coefficient (generalized Cox–Ingersoll–Ross model) demonstrates that the EKF type estimators may serve as efficient alternatives to simple maximum quasilikelihood approaches and Monte Carlo methods.