{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,7]],"date-time":"2024-09-07T21:49:59Z","timestamp":1725745799216},"publisher-location":"Berlin, Heidelberg","reference-count":19,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783642400193"},{"type":"electronic","value":"9783642400209"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2013]]},"DOI":"10.1007\/978-3-642-40020-9_53","type":"book-chapter","created":{"date-parts":[[2013,8,19]],"date-time":"2013-08-19T01:32:37Z","timestamp":1376875957000},"page":"487-494","source":"Crossref","is-referenced-by-count":0,"title":["Some Results on a \u03c7-divergence, an Extended Fisher Information and Generalized Cram\u00e9r-Rao Inequalities"],"prefix":"10.1007","author":[{"given":"Jean-Fran\u00e7ois","family":"Bercher","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"issue":"3","key":"53_CR1","doi-asserted-by":"publisher","first-page":"31101","DOI":"10.1103\/PhysRevE.68.031101","volume":"68","author":"S. Abe","year":"2003","unstructured":"Abe, S.: Geometry of escort distributions. Physical Review E\u00a068(3), 031101 (2003)","journal-title":"Physical Review E"},{"issue":"11","key":"53_CR2","doi-asserted-by":"publisher","first-page":"4925","DOI":"10.1109\/TIT.2009.2030485","volume":"55","author":"S.I. Amari","year":"2009","unstructured":"Amari, S.I.: \u03b1-divergence is unique, belonging to both f-divergence and Bregman divergence classes. IEEE Transactions on Information Theory\u00a055(11), 4925\u20134931 (2009)","journal-title":"IEEE Transactions on Information Theory"},{"issue":"4","key":"53_CR3","doi-asserted-by":"publisher","first-page":"477","DOI":"10.1214\/aoms\/1177729943","volume":"20","author":"E.W. Barankin","year":"1949","unstructured":"Barankin, E.W.: Locally best unbiased estimates. The Annals of Mathematical Statistics\u00a020(4), 477\u2013501 (1949)","journal-title":"The Annals of Mathematical Statistics"},{"key":"53_CR4","doi-asserted-by":"crossref","unstructured":"Beck, C., Schloegl, F.: Thermodynamics of Chaotic Systems. Cambridge University Press (1993)","DOI":"10.1017\/CBO9780511524585"},{"issue":"36","key":"53_CR5","doi-asserted-by":"publisher","first-page":"3235","DOI":"10.1016\/j.physleta.2009.07.015","volume":"373","author":"J.F. Bercher","year":"2009","unstructured":"Bercher, J.F.: Source coding with escort distributions and R\u00e9nyi entropy bounds. Physics Letters A\u00a0373(36), 3235\u20133238 (2009)","journal-title":"Physics Letters A"},{"issue":"15","key":"53_CR6","doi-asserted-by":"crossref","first-page":"3140","DOI":"10.1016\/j.physa.2013.03.062","volume":"392","author":"J.F. Bercher","year":"2013","unstructured":"Bercher, J.F.: Some properties of generalized Fisher information in the context of nonextensive thermostatistics. Physica A: Statistical Mechanics and its Applications 392(15), 3140\u20133154 (2013), http:\/\/hal.archives-ouvertes.fr\/hal-00766699","journal-title":"Physica A: Statistical Mechanics and its Applications"},{"key":"53_CR7","doi-asserted-by":"crossref","first-page":"095303","DOI":"10.1088\/1751-8113\/46\/9\/095303","volume":"46","author":"J.F. Bercher","year":"2013","unstructured":"Bercher, J.F.: On multidimensional generalized Cram\u00e9r-Rao inequalities, uncertainty relations and characterizations of generalized q-Gaussian distributions. Journal of Physics A: Mathematical and Theoretical 46(9), 095303 (2013), http:\/\/hal-upec-upem.archives-ouvertes.fr\/hal-00766695","journal-title":"Journal of Physics A: Mathematical and Theoretical"},{"issue":"12","key":"53_CR8","doi-asserted-by":"publisher","first-page":"1327","DOI":"10.1103\/PhysRevLett.62.1327","volume":"62","author":"A. Chhabra","year":"1989","unstructured":"Chhabra, A., Jensen, R.V.: Direct determination of the f(f(\u03b1)) singularity spectrum. Physical Review Letters\u00a062(12), 1327 (1989)","journal-title":"Physical Review Letters"},{"issue":"2","key":"53_CR9","doi-asserted-by":"publisher","first-page":"307","DOI":"10.1016\/S0001-8708(03)00080-X","volume":"182","author":"D. Cordero-Erausquin","year":"2004","unstructured":"Cordero-Erausquin, D., Nazaret, B., Villani, C.: A mass-transportation approach to sharp Sobolev and Gagliardo-Nirenberg inequalities. Advances in Mathematics\u00a0182(2), 307\u2013332 (2004)","journal-title":"Advances in Mathematics"},{"issue":"9","key":"53_CR10","doi-asserted-by":"publisher","first-page":"847","DOI":"10.1016\/S0021-7824(02)01266-7","volume":"81","author":"M. Pino Del","year":"2002","unstructured":"Del Pino, M., Dolbeault, J.: Best constants for Gagliardo-Nirenberg inequalities and applications to nonlinear diffusions. Journal de Math\u00e9matiques Pures et Appliqu\u00e9es\u00a081(9), 847\u2013875 (2002)","journal-title":"Journal de Math\u00e9matiques Pures et Appliqu\u00e9es"},{"key":"53_CR11","doi-asserted-by":"crossref","unstructured":"Liese, F., Miescke, K.J.: Statistical Decision Theory: Estimation, Testing, and Selection. Springer (June 2008)","DOI":"10.1007\/978-0-387-73194-0_3"},{"issue":"3","key":"53_CR12","doi-asserted-by":"publisher","first-page":"1319","DOI":"10.1109\/TIT.2011.2177563","volume":"58","author":"E. Lutwak","year":"2012","unstructured":"Lutwak, E., Lv, S., Yang, D., Zhang, G.: Extensions of Fisher information and Stam\u2019s inequality. IEEE Transactions on Information Theory\u00a058(3), 1319\u20131327 (2012)","journal-title":"IEEE Transactions on Information Theory"},{"issue":"5","key":"53_CR13","doi-asserted-by":"crossref","first-page":"051402","DOI":"10.1103\/PhysRevA.67.051402","volume":"67","author":"E. Lutz","year":"2003","unstructured":"Lutz, E.: Anomalous diffusion and Tsallis statistics in an optical lattice. Physical Review A 67(5), 051402 (2003)","journal-title":"Physical Review A"},{"key":"53_CR14","first-page":"012012","volume":"201","author":"A. Ohara","year":"2010","unstructured":"Ohara, A., Matsuzoe, H., Amari, S.I.: A dually flat structure on the space of escort distributions. Journal of Physics: Conference Series 201, 012012 (2010)","journal-title":"Journal of Physics: Conference Series"},{"issue":"4","key":"53_CR15","doi-asserted-by":"crossref","first-page":"537","DOI":"10.1140\/epjb\/e2008-00451-y","volume":"66","author":"V. Schw\u00e4mmle","year":"2008","unstructured":"Schw\u00e4mmle, V., Nobre, F.D., Tsallis, C.: q-Gaussians in the porous-medium equation: stability and time evolution. The European Physical Journal B-Condensed Matter and Complex Systems 66(4), 537\u2013546 (2008)","journal-title":"The European Physical Journal B-Condensed Matter and Complex Systems"},{"key":"53_CR16","doi-asserted-by":"crossref","unstructured":"Tsallis, C.: Introduction to Nonextensive Statistical Mechanics. Springer (April 2009)","DOI":"10.1007\/978-3-540-78961-1_2"},{"key":"53_CR17","unstructured":"Vajda, I.: \u03c7 a-divergence and generalized Fisher information. In: Transactions of the Sixth Prague Conference on Information Theory, Statistical Decision Functions and Random Processes, pp. 873\u2013886 (1973)"},{"key":"53_CR18","doi-asserted-by":"crossref","unstructured":"V\u00e1zquez, J.L.: Smoothing and Decay Estimates for Nonlinear Diffusion Equations: Equations of Porous Medium Type. Oxford University Press, USA (2006)","DOI":"10.1093\/acprof:oso\/9780199202973.001.0001"},{"issue":"2","key":"53_CR19","doi-asserted-by":"publisher","first-page":"338","DOI":"10.1109\/18.2647","volume":"34","author":"E. Weinstein","year":"1988","unstructured":"Weinstein, E., Weiss, A.: A general class of lower bounds in parameter estimation. IEEE Transactions on Information Theory\u00a034(2), 338\u2013342 (1988)","journal-title":"IEEE Transactions on Information Theory"}],"container-title":["Lecture Notes in Computer Science","Geometric Science of Information"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-40020-9_53","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,7,21]],"date-time":"2019-07-21T09:01:47Z","timestamp":1563699707000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-40020-9_53"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"ISBN":["9783642400193","9783642400209"],"references-count":19,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-40020-9_53","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2013]]}}}