Hosoya, Yuzo The second-order Fisher information. (English) Zbl 0638.62020 Biometrika 75, No. 2, 265-274 (1988). 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. Cited in 2 Documents MSC: 62E20 Asymptotic distribution theory in statistics 62F12 Asymptotic properties of parametric estimators Keywords:Edgeworth expansion; second-order efficiency; sufficiency; general second-order approximate formulae; Fisher information; asymptotically normal statistics; stationary time-series model; econometric simultaneous equation model; second-order conditional information; exponential family; location family; second-order ancillary statistic; second-order information loss; maximum likelihood estimate PDFBibTeX XMLCite \textit{Y. Hosoya}, Biometrika 75, No. 2, 265--274 (1988; Zbl 0638.62020) Full Text: DOI