Monte Carlo Resampling for Computation of the Fisher Information Matrix

• Activity Number: 273
• Type: Topic Contributed
• Date/Time: Wednesday, August 14, 2002 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Computing*
• Author(s): James Spall*+
• Affiliation(s): Johns Hopkins University
• Keywords: simultaneous perturbation ; Monte Carlo resampling ; parameter estimation ; experimental design ; bootstrap

Abstract

The Fisher information matrix plays a central role in the practice and theory of statistical estimation. This matrix provides a summary of the amount of information in the data relative to the quantities of interest. Some of the specific applications of the information matrix include confidence region calculation for parameter estimates, the determination of inputs in experimental design, providing a bound on the best possible performance in an adaptive system based on unbiased parameter estimates (such as a control system), and producing uncertainty bounds on predictions (such as from a neural network). Unfortunately, the analytical calculation of the information matrix is often a difficult or impossible task. This is especially the case with nonlinear statistical models, such as neural networks. This talk will describe a resampling-based method for computing the information matrix. This method applies in problems of arbitrary difficulty and is relatively easy to implement.