Relative Performance of Fisher Information in Interval Estimation

TL;DR

This paper compares the effectiveness of observed and expected Fisher information matrices in constructing confidence intervals for MLEs, demonstrating that the expected FIM generally yields more accurate estimates under certain conditions.

Contribution

It provides a theoretical comparison showing that confidence intervals based on the expected Fisher information are at least as accurate as those based on the observed Fisher information under specific criteria.

Findings

Expected FIM-based intervals are more accurate than observed FIM-based intervals.

Theoretical proof under certain conditions supports the superiority of expected FIM.

Analysis applies to multivariate parameters in statistical inference.

Abstract

Maximum likelihood estimates and corresponding confidence regions of the estimates are commonly used in statistical inference. In practice, people often construct approximate confidence regions with the Fisher information at given sample data based on the asymptotic normal distribution of the MLE (maximum likelihood estimate). Two common Fisher information matrices (FIMs, for multivariate parameters) are the observed FIM (the Hessian matrix of negative log-likelihood function) and the expected FIM (the expectation of the observed FIM). In this article, we prove that under certain conditions and with an MSE (mean-squared error) criterion, approximate confidence interval of each element of the MLE with the expected FIM is at least as accurate as that with the observed FIM.