On Monte Carlo methods for estimating the fisher information matrix in difficult problems

Abstract

The Fisher information matrix summarizes the amount of information in a set of data relative to the quantities of interest and forms the basis for the Cramér-Rao (lower) bound on the uncertainty in an estimate. There are many applications of the information matrix in modeling, systems analysis, and estimation. This paper presents a resampling-based method for computing the information matrix together with some new theory related to efficient implementation. We show how certain properties associated with the likelihood function and the error in the estimates of the Hessian matrix can be exploited to improve the accuracy of the Monte Carlo-based estimate of the information matrix.