Frequentist perspective on robust parameter estimation using the ensemble Kalman filter

Standard maximum likelihood or Bayesian approaches to parameter estimation of stochastic differential equations are not robust to perturbations in the continuous-in-time data. In this note, 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 two robust estimation techniques; namely subsampling the data and rough path corrections. We illustrate our findings through a simple numerical experiment.