NDLI: Relative performance of expected and observed fisher information in covariance estimation for maximum likelihood estimates

Content Provider	IEEE Xplore Digital Library
Author	Xumeng Cao Spall, J.C.
Copyright Year	2012
Description	Author affiliation: Dept. of Appl. Math. & Stat., Johns Hopkins Univ., Baltimore, MD, USA (Xumeng Cao; Spall, J.C.)
Abstract	Covariance matrix and confidence interval calculations for maximum likelihood estimates (MLEs) are commonly used in system identification and statistical inference. To accurately construct such confidence intervals, one typically needs to know the covariance of the MLE. Standard statistical theory tells that the normalized MLE is asymptotically normally distributed with mean zero and covariance being the inverse of the Fisher Information Matrix (FIM) at the unknown parameter. Two common estimates for the covariance of MLE are the inverse of the observed FIM (the same as the Hessian of negative log-likelihood) and the inverse of the expected FIM (the same as FIM). Both of the observed and expected FIM are evaluated at the MLE from the sample data. We show that, under reasonable conditions, the expected FIM outperforms the observed FIM under a mean squared error criterion. This result suggests that, with certain conditions, the expected FIM is a better estimate for the covariance of MLE in confidence interval calculations.
Sponsorship	IEEE Control Syst. Soc.
Starting Page	1871
Ending Page	1876
File Size	360864
Page Count	6
File Format	PDF
ISBN	9781457710957
ISSN	07431619
e-ISBN	9781457710964
e-ISBN	9781467321020
DOI	10.1109/ACC.2012.6315584
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2012-06-27
Publisher Place	Canada
Access Restriction	Subscribed
Rights Holder	American Automatic Control Council(AACC)
Subject Keyword	Maximum likelihood estimation Covariance matrix Vectors Approximation methods Zirconium Random variables observed Fisher information System identification parameter estimation covariance matrix mean squared error expected Fisher information
Content Type	Text
Resource Type	Article
Subject	Electrical and Electronic Engineering

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