On Two Forms of Fisher's Measure of Information

References

• Brown , L. ( 1982 ). A proof of the central limit theorem motivated by Cramer-Rao inequality . In: Kallianpur , G. , Krishnaiah , P. R. , Ghosh , J. K. , eds. Statistics and Probability: Essays in Honor of C. R. Rao . Amsterdam : North-Holland Publishing Co. . 141 – 148 .
   Google Scholar
• Carlen , E. E. ( 1991 ). Superadditivity of Fisher's information and logarithmic Sobolev inequalities . J. Functional Anal. 101 : 194 – 211 .
   Web of Science ®Google Scholar
• Cassela , G. , Berger , R. ( 2002 ). Statistical Inference . Belmont , California : Duxbury Press .
   Google Scholar
• DeCani , J. S. , Stine , R. A. ( 1986 ). A note on deriving the information matrix for a logistic distribution . Amer. Statistician 40 : 220 – 222 . [CSA]
   Web of Science ®Google Scholar
• Efron , B. F. , Hinkley , D. V. ( 1978 ). Assessing the accuracy of the maximum likelihood estimator: observed versus expected Fisher information . Biometrika 65 : 457 – 487 .
   Web of Science ®Google Scholar
• Ferentinos , K. , Papaioannou , T. ( 1981 ). New parametric measures of information . Information and Control 51 : 193 – 208 . [CROSSREF]
   Google Scholar
• Frieden , B. R. ( 1988 ). Applications to optics and wave mechnics of the criterion of maximum Cramer–Rao bound . J. Modern Optics 35 : 1297 – 1316 .
   Web of Science ®Google Scholar
• Frieden , B. R. ( 1998 ). Physics from Fisher Information–-A Unification . Cambridge , UK : Cambridge University Press .
   Google Scholar
• Itoh , Y. ( 1989 ). An application of the convolution inequality for the Fisher information . Ann. Instit. Statist. Math. 41 ( 1 ): 9 – 12 .
   Google Scholar
• Kagan , A. ( 2001 ). A discrete version of the Stam inequality and a characterization of the Poisson distribution . J. Statist. Plann. Inference 92 : 7 – 12 . [CROSSREF]
   Google Scholar
• Kagan , A. , Landsman , Z. ( 1997 ). Statistical meaning of Carlen's supperadditivity of the Fisher information . Statist. Probab. Lett. 32 : 175 – 179 . [CROSSREF]
   Web of Science ®Google Scholar
• Kagan , A. , Landsman , Z. ( 1999 ). Relation between the covariance and Fisher information matrices . Statist. Probab. Lett. 42 : 7 – 13 . [CROSSREF]
   Google Scholar
• Kapur , J. N. , Dhande , M. (1986). On the entropic measures of stochastic dependence. Ind. J. Pure Appl. Math. 17:581–595.
   Web of Science ®Google Scholar
• Lehmann , E. L. , Casella , G. ( 1998 ). Theory of Point Estimation . 2nd edn . New York : Springer-Verlag .
   Google Scholar
• Papaioannou , T. ( 1985 ). Measures of information . In: Kotz , S. S. , Johnson , N. L. , eds. Encyclopedia of Statistical Sciences . Vol. 5 , New York : John Wiley and Sons .
   Google Scholar
• Papaioannou , T. ( 2001 ). On distances and measures of information: a case of diversity . In: Charalambides , C. A. , Koutras , M. V. , Balakrishnan , N. , eds. Probability and Statistical Models with Applications . London : Chapman and Hall/CRC . 503 – 515 .
   Google Scholar
• Papathanasiou , V. ( 1993a ). An extension of the information inequality and related characterizations . Statist. Probab. Lett. 18 : 27 – 32 . [CROSSREF]
   Google Scholar
• Papathanasiou , V. ( 1993b ). Some characteristic properties of the Fisher information matrix via Cacoullos-type inequalities . J. Multivariate Anal. 44 : 256 – 265 . [CROSSREF]
   Web of Science ®Google Scholar
• Rao , B. R. ( 1958 ). On an analogue of Cramer-Rao inequality . Skand. Actuar. Tidskr 41 : 57 – 64 .
   Google Scholar
• Rothenberg , T. J. ( 1971 ). Identification of parametric models . Econometrika 39 : 577 – 591 .
   Web of Science ®Google Scholar
• Sankaran , M. ( 1964 ). On an analogue of Bhattacharya bound . Biometrika 51 : 268 – 270 .
   Google Scholar
• Stam , A. ( 1959 ). Some inequalities satisfied by the quantities of information of Fisher and Shannon . Information and Control 2 : 101 – 112 . [CROSSREF]
   Google Scholar
• Tambakis , D. ( 2001 ). Multivariate dependence at short horizons: asymmetric correlation form Fisher information . Mimeo , UK : Pembroke College, University of Cambridge, Cambridge .
   Google Scholar
• Zacks , S. ( 1971 ). The Theory of Statistical Inference . New York : John Wiley and Sons, Inc. .
   Google Scholar
• Zografos , K. ( 1998 ). On a measure of dependence based on Fisher's information matrix . Commun. Statist. Theory. Meth. 27 ( 7 ): 1715 – 1728 .
   Web of Science ®Google Scholar
• Zografos , K. ( 2000 ). Measures of multivariate dependence based on a distance between Fisher information matrices . J. Statist. Plann. Inference 89 : 91 – 107 . [CROSSREF]
   Google Scholar
• Zografos , K. , Ferentinos , K. , Papaioannou , T. ( 1989 ). Limiting properties of some measures of information . Ann. Instit. Statist. Math. 41 ( 3 ): 451 – 460 . [CROSSREF]
   Google Scholar