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Biometrika 1988 75(2):265-274; doi:10.1093/biomet/75.2.265
© 1988 by Biometrika Trust
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The second-order Fisher information

YUZO HOSOYA

Faculty of Economics, Tohoku University Kawauch, Sendai 980, Japan

The paper presents general second-order approximate formulae for the Fisher information of asymptotically normal statistics, and applies the formulae to a stationary time-series model as well as to an econometric simultaneous equation model. Also the second-order conditional information is evaluated for the exponential family and the location family. Conditioned on a second-order ancillary statistic, the second-order information loss of the maximum likelihood estimate is shown to be recovered.

Key Words: Asymptotic distribution • Conditionally • Edgeworth expansion • Fisher information • Information loss • Second-order efficiency • Sufficiency


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