{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,26]],"date-time":"2025-03-26T18:45:36Z","timestamp":1743014736753,"version":"3.40.3"},"publisher-location":"Cham","reference-count":12,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783319684444"},{"type":"electronic","value":"9783319684451"}],"license":[{"start":{"date-parts":[[2017,1,1]],"date-time":"2017-01-01T00:00:00Z","timestamp":1483228800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2017]]},"DOI":"10.1007\/978-3-319-68445-1_64","type":"book-chapter","created":{"date-parts":[[2017,10,24]],"date-time":"2017-10-24T00:40:36Z","timestamp":1508805636000},"page":"552-560","source":"Crossref","is-referenced-by-count":0,"title":["The Cram\u00e9r-Rao Inequality on Singular Statistical Models"],"prefix":"10.1007","author":[{"given":"H\u00f4ng V\u00e2n","family":"L\u00ea","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"J\u00fcrgen","family":"Jost","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lorenz","family":"Schwachh\u00f6fer","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2017,10,24]]},"reference":[{"key":"64_CR1","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1007\/s00440-014-0574-8","volume":"162","author":"N Ay","year":"2015","unstructured":"Ay, N., Jost, J., L\u00ea, H.V., Schwachh\u00f6fer, L.: Information geometry and sufficient statistics. Probab. Theory Relat. Fields 162, 327\u2013364 (2015)","journal-title":"Probab. Theory Relat. Fields"},{"key":"64_CR2","doi-asserted-by":"crossref","unstructured":"Ay, N., Jost, J., L\u00ea, H.V., Schwachh\u00f6fer, L.: Information Geometry. Springer (2017). Ergebnisse der Mathematik und ihrer Grenzgebiete","DOI":"10.1007\/978-3-319-56478-4"},{"key":"64_CR3","unstructured":"Ay, N., Jost, J., L\u00ea, H.V., Schwachh\u00f6fer, L.: Parametrized measure models. (accepted for Bernoulli Journal). arXiv:1510.07305"},{"key":"64_CR4","unstructured":"Amari, S., Nagaoka, H.: Methods of Information Geometry. Translations of Mathematical Monographs, vol. 191. American Mathematical Society (2000)"},{"key":"64_CR5","volume-title":"Efficient and Adaptive Estimation for Semiparametric Models","author":"P Bickel","year":"1998","unstructured":"Bickel, P., Klaassen, C.A.J., Ritov, Y., Wellner, J.A.: Efficient and Adaptive Estimation for Semiparametric Models. Springer, New York (1998)"},{"key":"64_CR6","unstructured":"Borovkov, A.A.: Mathematical Statistics. Gordon and Breach Science Publishers (1998)"},{"key":"64_CR7","doi-asserted-by":"crossref","unstructured":"Brown, L.D.: Fundamentals of Statistical Families with Applications in Statistical Decision Theory, Lecture Notes-Monograph Series, vol. 9. IMS (1986)","DOI":"10.1214\/lnms\/1215466757"},{"key":"64_CR8","volume-title":"Elements of Information Theory","author":"TM Cover","year":"2006","unstructured":"Cover, T.M., Thomas, J.A.: Elements of Information Theory, 2nd edn. Wiley, Hoboken (2006)","edition":"2"},{"key":"64_CR9","doi-asserted-by":"crossref","unstructured":"Fukumizu, K.: Exponential manifold by reproducing kernel Hilbert spaces. In: Gibilisco, P., Riccomagno, E., Rogantin, M.-P., Winn, H. (eds.) Algebraic and Geometric methods in Statistics, pp. 291\u2013306. Cambridge University Press (2009)","DOI":"10.1017\/CBO9780511642401.019"},{"key":"64_CR10","unstructured":"Jost, J., L\u00ea, H.V., Schwachh\u00f6fer, L.: The Cram\u00e9r-Rao inequality on singular statistical models I. arXiv:1703.09403"},{"key":"64_CR11","unstructured":"Jost, J., L\u00ea, H.V., Schwachh\u00f6fer, L.: The Cram\u00e9r-Rao inequality on singular statistical models II (2017, preprint)"},{"key":"64_CR12","doi-asserted-by":"crossref","first-page":"879","DOI":"10.1007\/s10463-016-0562-0","volume":"69","author":"HV L\u00ea","year":"2017","unstructured":"L\u00ea, H.V.: The uniqueness of the Fisher metric as information metric. AISM 69, 879\u2013896 (2017)","journal-title":"AISM"}],"container-title":["Lecture Notes in Computer Science","Geometric Science of Information"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-68445-1_64","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,8,27]],"date-time":"2023-08-27T13:05:50Z","timestamp":1693141550000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-319-68445-1_64"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017]]},"ISBN":["9783319684444","9783319684451"],"references-count":12,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-68445-1_64","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2017]]}}}