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Activity Number:
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228
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Type:
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Contributed
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Date/Time:
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Monday, August 3, 2009 : 2:00 PM to 3:50 PM
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Sponsor:
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Section on Statistics in Defense and National Security
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| Abstract - #305433 |
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Title:
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Expected and Observed Fisher Information in Variance Estimation for Maximum Likelihood Estimates
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Author(s):
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Xumeng Cao*+ and James C. Spall
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Companies:
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Johns Hopkins University and Johns Hopkins University Applied Physics Laboratory
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Address:
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Department of Applied Mathematics and Statistics, Baltimore, MD, 21210,
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Keywords:
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Parameter estimation ; expected Fisher information ; observed Fisher information ; variance ; mean-squared error
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Abstract:
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Confidence intervals (CIs) for the maximum likelihood estimates (MLEs) are commonly used in statistical inference. To accurately construct such CIs, typically one needs to know the distribution of the MLE. Standard statistical theory says the normalized MLE is asymptotically normal with mean zero and variance being a function of the Fisher Information Matrix (FIM) at the unknown parameter. Two common estimates for the variance are: the observed FIM (same as Hessian of negative log-likelihood) or the expected FIM, both of which are evaluated at the MLE given sample data. We show that the expected FIM tends to outperform the observed FIM under a mean-squared error criterion. This conclusion differs from that of several previous authors (Efron, Lindsay, etc.), where it was determined that the observed FIM is superior to the expected FIM; the reason for the difference will be discussed.
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