  The Fisher information matrix provides a way to measure the amount of
information given observed data based on parameters of interest. Many
applications of the FIM exist in statistical modeling, system identification,
and parameter estimation. We sometimes use the Monte Carlo-based method to
estimate the FIM because its analytical form is often impossible or difficult
to be computed in real-world models. In this paper, we review the basic method
based on simultaneous perturbations and present an enhanced resampling-based
method with independent simultaneous perturbations to estimate the Fisher
information matrix. We conduct theoretical and numerical analysis to show its
accuracy via variance reduction from $O(1/N)$ to $O(1/(nN))$, where $n$ is the
sample size of the data and $N$ is a measure of the Monte Carlo averaging. We
also consider the trade-off between accuracy and computational cost.
