Assessing the accuracy of the maximum likelihood estimator: Observed versus expected Fisher information

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ID: 300686
1978
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Abstract
This paper concerns normal approximations to the distribution of the maximum likelihood estimator in one-parameter families. The traditional variance approximation is 1/§, where θ is the maximum likelihood estimator and § is the expected total Fisher information. Many writers, including R. A. Fisher, have argued in favour of the variance estimate 1/I(x), where I(x) is the observed information, i.e. minus the second derivative of the log likelihood function at θ given data x. We give a frequentist justification for preferring 1/I(x) to 1/§. The former is shown to approximate the conditional variance of 8 given an appropriate ancillary statistic which to a first approximation is I(x). The theory may be seen to flow naturally from Fisher's pioneering papers on likelihood estimation. A large number of examples are used to supplement a small amount of theory. Our evidence indicates preference for the likelihood ratio method of obtaining confidence limits.
Reference Key
openalex_W2067342226 Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Bradley Efron, D. V. Hinkley
Journal jurnal biometrika dan kependudukan
Year 1978
DOI
10.1093/biomet/65.3.457
URL
https://doi.org/10.1093/biomet/65.3.457
Keywords Keywords not found

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