Newton-based maximum likelihood estimation in nonlinear state space models
This work addresses a specific computational bottleneck in statistical inference for nonlinear state space models, offering incremental improvements in parameter estimation methods.
The paper tackled the challenge of maximum likelihood estimation in nonlinear state space models by developing Newton-based methods using Fisher's identity and smoothing algorithms, with results showing encouraging performance on simulated data from two models.
Maximum likelihood (ML) estimation using Newton's method in nonlinear state space models (SSMs) is a challenging problem due to the analytical intractability of the log-likelihood and its gradient and Hessian. We estimate the gradient and Hessian using Fisher's identity in combination with a smoothing algorithm. We explore two approximations of the log-likelihood and of the solution of the smoothing problem. The first is a linearization approximation which is computationally cheap, but the accuracy typically varies between models. The second is a sampling approximation which is asymptotically valid for any SSM but is more computationally costly. We demonstrate our approach for ML parameter estimation on simulated data from two different SSMs with encouraging results.