Salicrú, Miquel Measures of information associated with Csiszár’s divergences. (English) Zbl 0837.94007 Kybernetika 30, No. 5, 563-573 (1994). Measures of information associated with Csiszár’s divergences are obtained. If the parameter is univariate the information measures are revised and completed. In the multivariate case two alternatives are presented: In the first case the author considers the matrix defining the metric in direction to the tangent space, as information matrix, associated to a predefined distance. The second alternative consists in defining the elements of the information matrix, based on the distance between a given distribution, and the result of disturbing the parameter into two directions. Reviewer: L.Pardo (Madrid) Cited in 3 Documents MSC: 94A17 Measures of information, entropy 62B10 Statistical aspects of information-theoretic topics Keywords:divergences measures; Fisher’s information; information measures PDF BibTeX XML Cite \textit{M. Salicrú}, Kybernetika 30, No. 5, 563--573 (1994; Zbl 0837.94007) Full Text: EuDML Link OpenURL References: [1] J. Aggarwal: Sur l’information de Fisher. Théories de l’Information (J. Kampé de Fériet, Springer-Verlag, Berlin–New York 1974, pp. 111-117. · Zbl 0299.94016 [2] S. Amari: Differential-Geometric Methods in Statistics. (Lecture Notes in Statistics 28.) Springer-Verlag, Berlin–New York 1985. · Zbl 0559.62001 [3] D. E. Boekee: The \(D_f\) information of order \(s\). Trans, of the Eighth Prague Conference, Academia, Prague 1978, Vol. C, pp. 55-66. [4] J. Burbea: Informative geometry in probability spaces. Exposition. Math. 4 (1986), 345-365. · Zbl 0604.62006 [5] J. Burbea, C. R. Rao: Entropy differential metric, distance and divergence measures in probability spaces: a unified approach. J. Multivariate Anal. 12 (1982), 575-596. · Zbl 0526.60015 [6] K. Ferentinos, T. Papaioannou: New parametric measures of information. Inform. and Control 51 (1981), 193-208. · Zbl 0524.62005 [7] C. Fourgeaud, A. Fuchs: Statistique. Dunod, Paris 1972. · Zbl 0234.62001 [8] A. M. Kagan: On the theory of Fisher’s amount of information. Soviet Math. Dokl. 4 (1963), 991-993. · Zbl 0138.14902 [9] C. R. Rao: Differential metrics in probability spaces. Differential Geometry in Statistical Inference (Shanti S. Gupta, series, 1987, pp. 217-240. [10] C. R. Rao: Linear Statistical Inference and its Applications. Wiley, New York 1973. · Zbl 0256.62002 [11] M. Salicrú: Medidas de divergencia en an lisis de datos (Tesis doctoral.). Univ. Barcelona 1987. [12] M. Salicrú: Matrices Riemanianas asociadas a M-divergencias. XVII Congreso SEIO, 1988, pp. 51-54. [13] M. Salicrú: Matrices informativas asociadas a medidas de Csiszár. XVIII Congreso SEIO, 1989, pp. 462-467. [14] M. Salicrú, P. Sanchez: Matrices informativas asociadas a J-divergencias. II Conferencia española de Biometria, 1989, pp. 249-251. [15] I. Vajda: \(\chi^2\)-divergence and generalized Fisher’s information. Trans. of the Sixth Prague Conference, Academia, Prague 1971, pp. 873-886. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.