{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,7]],"date-time":"2024-09-07T21:50:42Z","timestamp":1725745842696},"publisher-location":"Berlin, Heidelberg","reference-count":20,"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_82","type":"book-chapter","created":{"date-parts":[[2013,8,19]],"date-time":"2013-08-19T01:32:37Z","timestamp":1376875957000},"page":"737-742","source":"Crossref","is-referenced-by-count":2,"title":["A Riemannian Geometry in the q-Exponential Banach Manifold Induced by q-Divergences"],"prefix":"10.1007","author":[{"given":"G.","family":"Loaiza","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"H. R.","family":"Quiceno","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"82_CR1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-5056-2","volume-title":"Differential-geometrical methods in statistics","author":"S. Amari","year":"1985","unstructured":"Amari, S.: Differential-geometrical methods in statistics. Springer, New York (1985)"},{"key":"#cr-split#-82_CR2.1","unstructured":"Amari, S., Nagaoka, H.: Methods of information Geometry. American Mathematical Society, RI (2000);"},{"key":"#cr-split#-82_CR2.2","unstructured":"Translated from the 1993 Japanese original by Daishi Harada, Providence"},{"key":"82_CR3","doi-asserted-by":"publisher","first-page":"1170","DOI":"10.3390\/e13061170","volume":"13","author":"S. Amari","year":"2011","unstructured":"Amari, S., Ohara, A.: Geometry of q-exponential family of probability distributions. Entropy\u00a013, 1170\u20131185 (2011)","journal-title":"Entropy"},{"key":"82_CR4","unstructured":"Borges, E.P.: Manifesta\u00f5es din\u00e2micas e termodin\u00e2micas de sistemas n\u00e3o-extensivos. Tese de Dutorado, Centro Brasileiro de Pesquisas Fisicas, Rio de Janeiro (2004)"},{"key":"82_CR5","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1007\/s10463-006-0096-y","volume":"59","author":"A. Cena","year":"2006","unstructured":"Cena, A., Pistone, G.: Exponential statistical manifold. Annals of the Institute of Statistical Mathematics\u00a059, 27\u201356 (2006)","journal-title":"Annals of the Institute of Statistical Mathematics"},{"key":"82_CR6","doi-asserted-by":"crossref","first-page":"248","DOI":"10.1111\/j.2517-6161.1975.tb01540.x","volume":"37","author":"A.P. Dawid","year":"1975","unstructured":"Dawid, A.P.: On the conceptsof sufficiency and ancillarity in the presence of nuisance parameters. Journal of the Royal Statistical Society B\u00a037, 248\u2013258 (1975)","journal-title":"Journal of the Royal Statistical Society B"},{"key":"82_CR7","doi-asserted-by":"publisher","first-page":"1189","DOI":"10.1214\/aos\/1176343282","volume":"3","author":"B. Efron","year":"1975","unstructured":"Efron, B.: Defining the curvature of a statistical problem (with applications to second order efficiency). Annals of Statistics\u00a03, 1189\u20131242 (1975)","journal-title":"Annals of Statistics"},{"key":"82_CR8","doi-asserted-by":"publisher","first-page":"793","DOI":"10.1214\/aos\/1176346246","volume":"11","author":"S. Eguchi","year":"1983","unstructured":"Eguchi, S.: Second order efficiency of minimum coontrast estimator in a curved exponential family. Annals of Statistics\u00a011, 793\u2013803 (1983)","journal-title":"Annals of Statistics"},{"key":"82_CR9","doi-asserted-by":"publisher","first-page":"4868","DOI":"10.1063\/1.1805729","volume":"45","author":"S. Furuichi","year":"2004","unstructured":"Furuichi, S.: Fundamental properties of Tsallis relative entropy. J. Math. Phys.\u00a045, 4868\u20134877 (2004)","journal-title":"J. Math. Phys."},{"key":"82_CR10","doi-asserted-by":"publisher","first-page":"325","DOI":"10.1142\/S021902579800017X","volume":"1","author":"P. Gibilisco","year":"1998","unstructured":"Gibilisco, P., Pistone, G.: Connections on non-parametric statistical manifolds by Orlicz space geometry. Infinite Dimensional Analysis Quantum Probability and Related Topics\u00a01, 325\u2013347 (1998)","journal-title":"Infinite Dimensional Analysis Quantum Probability and Related Topics"},{"key":"82_CR11","doi-asserted-by":"publisher","first-page":"453","DOI":"10.1098\/rspa.1946.0056","volume":"186","author":"H. Jeffreys","year":"1946","unstructured":"Jeffreys, H.: An invariant form for the prior probability in estimation problems. Proceedings of Royal Society A\u00a0186, 453\u2013461 (1946)","journal-title":"Proceedings of Royal Society A"},{"key":"82_CR12","series-title":"series in Banach spaces","volume-title":"Conditional and undconditional convergence, Traslated for the Russian by Andrei Iacob","author":"M.I. Kadets","year":"1997","unstructured":"Kadets, M.I., Kadets, V.M.: Conditional and undconditional convergence, Traslated for the Russian by Andrei Iacob. series in Banach spaces. Birkaaauser, Basel (1997)"},{"key":"82_CR13","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1214\/aoms\/1177729694","volume":"22","author":"S. Kulback","year":"1951","unstructured":"Kulback, S., Leibler, R.A.: On Information and Sufficiency. Annals of Mathematics and Statistics\u00a022, 79\u201386 (1951)","journal-title":"Annals of Mathematics and Statistics"},{"key":"82_CR14","doi-asserted-by":"publisher","first-page":"446","DOI":"10.1016\/j.jmaa.2012.08.046","volume":"398","author":"G. Loaiza","year":"2013","unstructured":"Loaiza, G., Quiceno, H.R.: A q-exponential statistical Banach manifold. Journal of Mathematical Analysis and Applications\u00a0398, 446\u2013476 (2013)","journal-title":"Journal of Mathematical Analysis and Applications"},{"key":"82_CR15","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1140\/epjb\/e2009-00154-y","volume":"70","author":"G. Pistone","year":"2009","unstructured":"Pistone, G.: k-exponential models from the geometrical viewpoint. The European Physical Journal B\u00a070, 29\u201337 (2009)","journal-title":"The European Physical Journal B"},{"issue":"5","key":"82_CR16","doi-asserted-by":"publisher","first-page":"1543","DOI":"10.1214\/aos\/1176324311","volume":"23","author":"G. Pistone","year":"1995","unstructured":"Pistone, G., Sempi, C.: An infinite-dimensional geometric structure on the space of all the probability measures equivalent to a given one. The Annals of Statistics\u00a023(5), 1543\u20131561 (1995)","journal-title":"The Annals of Statistics"},{"key":"82_CR17","first-page":"81","volume":"37","author":"C.R. Rao","year":"1945","unstructured":"Rao, C.R.: Information and accuracy attainable in estimation of statistical parameters. Bull. Calcutta Math. Soc.\u00a037, 81\u201391 (1945)","journal-title":"Bull. Calcutta Math. Soc."},{"key":"82_CR18","doi-asserted-by":"publisher","first-page":"479","DOI":"10.1007\/BF01016429","volume":"52","author":"C. Tsallis","year":"1988","unstructured":"Tsallis, C.: Possible generalization of Boltzmann-Gibbs statistics. J.Stat. Phys.\u00a052, 479\u2013487 (1988)","journal-title":"J.Stat. Phys."},{"key":"82_CR19","unstructured":"Zhang, J.: Referential duality and representational duality on statistical manifolds. In: 2nd International Symposium on Information Geometry and its Applications, Tokyo, pp. 58\u201367 (2005)"}],"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_82","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,5,16]],"date-time":"2024-05-16T20:10:49Z","timestamp":1715890249000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-40020-9_82"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"ISBN":["9783642400193","9783642400209"],"references-count":20,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-40020-9_82","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2013]]}}}