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Activity Number: 651
Type: Contributed
Date/Time: Thursday, August 4, 2016 : 8:30 AM to 10:20 AM
Sponsor: Section on Statistical Computing
Abstract #319004 View Presentation
Title: Accuracy Analysis of Unbiased Estimations for Fisher Information in the Scalar Case
Author(s): Shenghan Guo* and James C. Spall
Companies: The Johns Hopkins University and The Johns Hopkins University
Keywords: Fisher information number ; the Central Limit Theorem ; Taylor expansion
Abstract:

The Fisher information matrix (FIM) has long been of interest in statistics and computational mathematics for its various uses. Its scalar case, the Fisher information number (FIN), is also widely used. However, in many cases it is challenging to obtain the true value for the Fisher information so we need to use the unbiased estimation as a proxy.

In this paper, we compare the accuracy of two unbiased estimations for FIN, i.e. the sample mean of squared gradient and the sample mean of second-order derivative of log-likelihood. A set of sufficient conditions are deducted, based on which we can judge the accuracy of each estimation. The conclusion will be case sensitive, meaning that either method can be more accurate than the other depending on the density function.

Three examples are provided in numerical study as illustrations to our analysis. We look at independent and identically distributed samples from Laplace distribution and normal distribution, respectively. We also look at a signal-plus problem that features an independent but non-identically distributed samples.


Authors who are presenting talks have a * after their name.

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