Improved Monte Carlo Estimation of the Fisher Information Matrix with Independent Perturbations

The Fisher information matrix provides a way to measure the amount of information given observed data based on parameters of interest. There are many relative applications in statistical modeling, system identification, and parameter estimation. This article presents an enhanced resampling-based method with independent perturbation to estimate the Fisher information matrix. We show its accuracy via variance reduction that is reduced by a factor of $n$, where $n$ is the sample size, with a numerical example under the signal-plus-noise setting also illustrating same.