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The second-order Fisher information. (English) Zbl 0638.62020

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.

MSC:

62E20 Asymptotic distribution theory in statistics
62F12 Asymptotic properties of parametric estimators
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