Unbiased estimation of the Hessian for partially observed diffusions.

ABSTRACT: In this article, we consider the development of unbiased estimators of the Hessian, of the log-likelihood function with respect to parameters, for partially observed diffusion processes. These processes arise in numerous applications, where such diffusions require derivative information, either through the Jacobian or Hessian matrix. As time-discretizations of diffusions induce a bias, we provide an unbiased estimator of the Hessian. This is based on using Girsanov's Theorem and randomization schemes developed through Mcleish (2011 Monte Carlo Methods Appl. 17, 301-315 (doi:10.1515/mcma.2011.013)) and Rhee & Glynn (2016 Op. Res. 63, 1026-1043). We demonstrate our developed estimator of the Hessian is unbiased, and one of finite variance. We numerically test and

SUBMITTER: Chada NK 

PROVIDER: S-EPMC9215219 | biostudies-literature | 2022 Jun

REPOSITORIES: biostudies-literature