Standard maximum likelihood or Bayesian approaches to parameter estimation for stochastic differential equations are not robust to perturbations in the continuous-in-time data. In this paper, we give a rather elementary explanation of this observation in the context of continuous-time parameter estimation using an ensemble Kalman filter. We employ the frequentist perspective to shed new light on three robust estimation techniques; namely subsampling the data, rough path corrections, and data filtering. We illustrate our findings through a simple numerical experiment.

翻译：标准最大似然估计或贝叶斯参数估计方法在应用于随机微分方程时，对连续时间数据中的扰动缺乏鲁棒性。本文从连续时间参数估计的视角出发，基于集成卡尔曼滤波器对这一现象给出了较为基础性的解释。我们采用频率学派观点，为三种鲁棒估计技术——即数据子采样、粗糙路径修正和数据滤波——提供了新的理解。通过一个简单的数值实验，我们对研究结果进行了验证。