{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,24]],"date-time":"2025-09-24T00:18:20Z","timestamp":1758673100497,"version":"3.44.0"},"publisher-location":"Cham","reference-count":34,"publisher":"Springer Nature Switzerland","isbn-type":[{"type":"print","value":"9783031689482"},{"type":"electronic","value":"9783031689499"}],"license":[{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025]]},"DOI":"10.1007\/978-3-031-68949-9_22","type":"book-chapter","created":{"date-parts":[[2025,1,10]],"date-time":"2025-01-10T17:58:45Z","timestamp":1736531925000},"page":"295-308","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A New Class of Conditional Tail Expectation Estimators"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4881-4188","authenticated-orcid":false,"given":"L\u00edgia","family":"Henriques-Rodrigues","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2903-6993","authenticated-orcid":false,"given":"M. Ivette","family":"Gomes","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0255-4106","authenticated-orcid":false,"given":"Fernanda","family":"Figueiredo","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8628-7281","authenticated-orcid":false,"given":"Frederico","family":"Caeiro","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,1,11]]},"reference":[{"key":"22_CR1","unstructured":"Morgan, J.P.: Riskmetrics-Technical Document, 4th edn. Morgan Guaranty Trust Company of New York, J.P.Morgan\/Reuters (1996). https:\/\/www.msci.com\/documents\/10199\/5915b101-4206-4ba0-aee2-3449d5c7e95a"},{"issue":"3","key":"22_CR2","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1111\/1467-9965.00068","volume":"9","author":"P Artzner","year":"1999","unstructured":"Artzner, P., Delbaen, F., Eber, J.M., Heath, D.: Coherent measures of risk. Math. Finance 9(3), 203\u2013228 (1999). https:\/\/doi.org\/10.1111\/1467-9965.00068","journal-title":"Math. Finance"},{"key":"22_CR3","doi-asserted-by":"crossref","unstructured":"Denuit, M., Dhaene, J., Goovaerts, M., Kaas, R.: Actuarial Theory for Dependent Risks: Measures, Orders and Models. Wiley, Hoboken (2006). https:\/\/doi.org\/10.1002\/0470016450","DOI":"10.1002\/0470016450"},{"key":"22_CR4","volume-title":"An Introduction To Mathematical Risk Theory","author":"HU Gerber","year":"1979","unstructured":"Gerber, H.U.: An Introduction To Mathematical Risk Theory. R Irwin, Philadelphia (1979)"},{"key":"22_CR5","first-page":"68","volume":"10","author":"P Artzner","year":"1997","unstructured":"Artzner, P., Delbaen, F., Eber, J.M., Heath, D.: Thinking coherently. Risk 10, 68\u201371 (1997)","journal-title":"Risk"},{"key":"22_CR6","volume-title":"An introduction to risk measures for actuarial applications","author":"MR Hardy","year":"2006","unstructured":"Hardy, M.R.: An introduction to risk measures for actuarial applications. Tech. rep., University of Waterloo (2006). https:\/\/www.casact.org\/sites\/default\/files\/database\/studynotes_hardy4.pdf"},{"key":"22_CR7","doi-asserted-by":"publisher","first-page":"62","DOI":"10.1080\/10920277.2004.10596171","volume":"8","author":"MR Hardy","year":"2004","unstructured":"Hardy, M.R., Wirch, J.L.: The iterated CTE: a dynamic risk measure. North Am. Actuar. J. 8, 62\u201375 (2004). https:\/\/doi.org\/10.1080\/10920277.2004.10596171","journal-title":"North Am. Actuar. J."},{"key":"22_CR8","first-page":"26","volume":"5","author":"E Valdez","year":"2005","unstructured":"Valdez, E.: Tail conditional variance for elliptically contoured distributions. Belg. Actuar. Bull. 5, 26\u201336 (2005). https:\/\/api.semanticscholar.org\/CorpusID:54083815","journal-title":"Belg. Actuar. Bull."},{"key":"22_CR9","doi-asserted-by":"publisher","first-page":"433","DOI":"10.2143\/AST.36.2.2017929","volume":"36","author":"E Furman","year":"2006","unstructured":"Furman, E., Landsman, Z.: Tail variance premium with applications for elliptical portfolio of risks. Astin Bull. 36, 433\u2013462 (2006). https:\/\/doi.org\/10.2143\/AST.36.2.2017929","journal-title":"Astin Bull."},{"key":"22_CR10","first-page":"147","volume":"10","author":"J Hong","year":"2010","unstructured":"Hong, J., Elshahat, A.: Conditional tail variance and conditional tail skewness. J. Financ. Econ. Pract. 10, 147\u2013156 (2010)","journal-title":"J. Financ. Econ. Pract."},{"key":"22_CR11","doi-asserted-by":"publisher","first-page":"988","DOI":"10.1111\/sjos.12078","volume":"41","author":"JE Methni","year":"2014","unstructured":"Methni, J.E., Gardes, L., Girard, S.: Non-parametric estimation of extreme risk measures from conditional heavy-tailed distributions. Scand. J. Stat. 41, 988\u20131012 (2014). https:\/\/doi.org\/10.1111\/sjos.12078","journal-title":"Scand. J. Stat."},{"key":"22_CR12","doi-asserted-by":"publisher","first-page":"102","DOI":"10.1016\/j.insmatheco.2022.08.003","volume":"107","author":"Y Goegebeur","year":"2022","unstructured":"Goegebeur, Y., Guillou, A., Pedersen, T., Qin, J.: Extreme-value based estimation of the conditional tail moment with application to reinsurance rating. Insur. Math. Econ. 107, 102\u2013122 (2022). https:\/\/doi.org\/10.1016\/j.insmatheco.2022.08.003","journal-title":"Insur. Math. Econ."},{"key":"22_CR13","first-page":"180","volume":"24","author":"RA Fisher","year":"1928","unstructured":"Fisher, R.A., Tippett, L.H.C.: Limiting forms of the frequency distribution of the largest or smallest members of a sample. In: Proceedings of the Cambridge Philosophical Society, vol. 24, pp. 180\u2013190 (1928). https:\/\/doi.org\/10.1017\/S0305004100015681","journal-title":"In: Proceedings of the Cambridge Philosophical Society"},{"key":"22_CR14","doi-asserted-by":"crossref","unstructured":"de Haan, L.: Slow variation and characterization of domains of attraction. In: Statistical Extremes and Applications, pp. 31\u201348. Springer Netherlands (1984). https:\/\/doi.org\/10.1007\/978-94-017-3069-3_4","DOI":"10.1007\/978-94-017-3069-3_4"},{"key":"22_CR15","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1111\/j.2517-6161.1982.tb01183.x","volume":"44","author":"P Hall","year":"1982","unstructured":"Hall, P.: On some simple estimates of an exponent of regular variation. J. R. Stat. Soc. B 44, 37\u201342 (1982). https:\/\/doi.org\/10.1111\/j.2517-6161.1982.tb01183.x","journal-title":"J. R. Stat. Soc. B"},{"key":"22_CR16","doi-asserted-by":"publisher","first-page":"333","DOI":"10.1214\/aos\/1176346596","volume":"13","author":"P Hall","year":"1985","unstructured":"Hall, P., Welsh, A.H.: Adaptive estimates of parameters of regular variation. Ann. Stat. 13, 333\u2013341 (1985). https:\/\/doi.org\/10.1214\/aos\/1176346596","journal-title":"Ann. Stat."},{"issue":"1\u20132","key":"22_CR17","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1016\/S0378-3758(00)00201-9","volume":"93","author":"MI Gomes","year":"2001","unstructured":"Gomes, M.I., Martins, M.J.: Generalizations of the Hill estimator \u2013 asymptotic versus finite sample behaviour. J. Stat. Plan. Inference 93(1\u20132), 161\u2013180 (2001). https:\/\/doi.org\/10.1016\/s0378-3758(00)00201-9","journal-title":"J. Stat. Plan. Inference"},{"key":"22_CR18","doi-asserted-by":"publisher","unstructured":"Hill, B.M.: A simple general approach to inference about the tail of a distribution. Ann. Stat. 3(5) (1975). https:\/\/doi.org\/10.1214\/aos\/1176343247","DOI":"10.1214\/aos\/1176343247"},{"key":"22_CR19","doi-asserted-by":"publisher","first-page":"60","DOI":"10.1111\/1467-9574.00068","volume":"52","author":"L de Haan","year":"1998","unstructured":"de Haan, L., Peng, L.: Comparison of tail index estimators. Stat. Neerlandica 52, 60\u201370 (1998). https:\/\/doi.org\/10.1111\/1467-9574.00068","journal-title":"Stat. Neerlandica"},{"issue":"11","key":"22_CR20","doi-asserted-by":"publisher","first-page":"3590","DOI":"10.1016\/j.jspi.2005.11.011","volume":"138","author":"V Brazauskas","year":"2008","unstructured":"Brazauskas, V., Jones, B.L., Puri, M.L., Zitikis, R.: Estimating conditional tail expectation with actuarial applications in view. J. Stat. Plan. Inference 138(11), 3590\u20133604 (2008). https:\/\/doi.org\/10.1016\/j.jspi.2005.11.011","journal-title":"J. Stat. Plan. Inference"},{"key":"22_CR21","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1155\/2010\/596839","volume":"2010","author":"A Necir","year":"2010","unstructured":"Necir, A., Rassoul, A., Zitikis, R.: Estimating the conditional tail expectation in the case of heavy-tailed losses. J. Probab. Stat. 2010, 1\u201317 (2010). https:\/\/doi.org\/10.1155\/2010\/596839","journal-title":"J. Probab. Stat."},{"key":"22_CR22","doi-asserted-by":"crossref","unstructured":"Deme, E.H., Girard, S., Guillou, A.: Reduced-bias estimator of the conditional tail expectation of heavy-tailed distributions. In: Mathematical Statistics and Limit Theorems, pp. 105\u2013123. Springer International Publishing (2015). https:\/\/doi.org\/10.1007\/978-3-319-12442-1_7","DOI":"10.1007\/978-3-319-12442-1_7"},{"issue":"1","key":"22_CR23","doi-asserted-by":"publisher","first-page":"99","DOI":"10.19139\/soic-2310-5070-665","volume":"8","author":"M Laidi","year":"2020","unstructured":"Laidi, M., Rassoul, A., Rouis, O.: Improved estimator of the conditional tail expectation in the case of heavy-tailed losses. Stat. Optim. Inf. Comput. 8(1), 99\u2013109 (2020). https:\/\/doi.org\/10.19139\/soic-2310-5070-665","journal-title":"Stat. Optim. Inf. Comput."},{"key":"22_CR24","doi-asserted-by":"publisher","first-page":"698","DOI":"10.1016\/j.insmatheco.2013.09.004","volume":"53","author":"A Rassoul","year":"2013","unstructured":"Rassoul, A.: Kernel-type estimator of the conditional tail expectation for a heavy-tailed distribution. Insur. Math. Econ. 53, 698\u2013703 (2013). https:\/\/doi.org\/10.1016\/j.insmatheco.2013.09.004","journal-title":"Insur. Math. Econ."},{"issue":"16","key":"22_CR25","first-page":"1","volume":"15","author":"DL Bouali","year":"2021","unstructured":"Bouali, D.L., Benatia, F., Brahimi, B., Chesneau, C.: Robust estimator of conditional tail expectation of Pareto-type distributions. J. Stat. Theory Pract. 15(16), 1\u201312 (2021). https:\/\/doi.org\/10.1007\/s42519-020-00153-0","journal-title":"J. Stat. Theory Pract."},{"key":"22_CR26","unstructured":"Fabi\u00e1n, Z., Stehl\u00edk, M.: On robust and distribution sensitive Hill like method. Tech. rep., IFAS research report (2009). http:\/\/ifas.jku.at\/research-paper-series\/IFAS-2009-43.pdf"},{"key":"22_CR27","doi-asserted-by":"crossref","unstructured":"Gomes, M.I., Figueiredo, F., Henriques-Rodrigues, L.: Reliable alternative ways to manage the risk of extreme events. In: Statistical Modelling and Risk Analysis, Springer Proceedings in Mathemtics and Statistics 430. Springer Netherlands (2023). https:\/\/doi.org\/10.1007\/978-3-031-39864-3_8","DOI":"10.1007\/978-3-031-39864-3_8"},{"issue":"1","key":"22_CR28","doi-asserted-by":"publisher","first-page":"518","DOI":"10.1016\/j.csda.2012.07.019","volume":"57","author":"MF Brilhante","year":"2013","unstructured":"Brilhante, M.F., Gomes, M.I., Pestana, D.: A simple generalisation of the Hill estimator. Comput. Stat. Data Anal. 57(1), 518\u2013535 (2013). https:\/\/doi.org\/10.1016\/j.csda.2012.07.019","journal-title":"Comput. Stat. Data Anal."},{"issue":"1","key":"22_CR29","doi-asserted-by":"publisher","first-page":"336","DOI":"10.1007\/s10986-013-9212-x","volume":"53","author":"V Paulauskas","year":"2013","unstructured":"Paulauskas, V., Vai\u010diulis, M.: On an improvement of Hill and some other estimators. Lithuanian Math. J. 53(1), 336\u2013355 (2013). https:\/\/doi.org\/10.1007\/s10986-013-9212-x","journal-title":"Lithuanian Math. J."},{"issue":"1","key":"22_CR30","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1007\/s10463-013-0412-2","volume":"66","author":"J Beran","year":"2013","unstructured":"Beran, J., Schell, D., Stehl\u00edk, M.: The harmonic moment tail index estimator: asymptotic distribution and robustness. Ann. Inst. Stat. Math. 66(1), 193\u2013220 (2013). https:\/\/doi.org\/10.1007\/s10463-013-0412-2","journal-title":"Ann. Inst. Stat. Math."},{"issue":"1\u20132","key":"22_CR31","doi-asserted-by":"publisher","first-page":"15","DOI":"10.1016\/S0378-3758(00)00321-9","volume":"98","author":"J Segers","year":"2001","unstructured":"Segers, J.: Residual estimators. J. Stat. Plan. Inference 98(1\u20132), 15\u201327 (2001). https:\/\/doi.org\/10.1016\/s0378-3758(00)00321-9","journal-title":"J. Stat. Plan. Inference"},{"issue":"364","key":"22_CR32","first-page":"812","volume":"73","author":"I Weissman","year":"1978","unstructured":"Weissman, I.: Estimation of parameters and larger quantiles based on the k largest observations. J. Am. Stat. Assoc. 73(364), 812 (1978). https:\/\/doi.org\/10.2307\/2286285","journal-title":"J. Am. Stat. Assoc."},{"key":"22_CR33","doi-asserted-by":"publisher","first-page":"656","DOI":"10.1073\/pnas.17.2.656","volume":"17","author":"GD Birkhoff","year":"1931","unstructured":"Birkhoff, G.D.: Proof of the ergodic theorem. Proc. Natl. Acad. Sci. 17, 656\u2013660 (1931). https:\/\/doi.org\/10.1073\/pnas.17.2.656","journal-title":"Proc. Natl. Acad. Sci."},{"key":"22_CR34","doi-asserted-by":"crossref","unstructured":"Lindley, D.V.: Mathematical statistics, by A. A. Borovkov (translated from the Russian by A. Moullagaliev), pp. 570. \u00a389. 1998. ISBN 90 5699 018 7 (Gordon and Breach: Amsterdam). Math. Gazette 83(497), 374\u2013374 (1999). https:\/\/doi.org\/10.2307\/3619119","DOI":"10.2307\/3619119"}],"container-title":["Springer Proceedings in Mathematics &amp; Statistics","New Frontiers in Statistics and Data Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-031-68949-9_22","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,23]],"date-time":"2025-09-23T16:22:59Z","timestamp":1758644579000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-68949-9_22"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025]]},"ISBN":["9783031689482","9783031689499"],"references-count":34,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-68949-9_22","relation":{},"ISSN":["2194-1009","2194-1017"],"issn-type":[{"type":"print","value":"2194-1009"},{"type":"electronic","value":"2194-1017"}],"subject":[],"published":{"date-parts":[[2025]]},"assertion":[{"value":"11 January 2025","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"SPE","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Congress of the Portuguese Statistical Society","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Evora","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Portugal","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2021","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"13 October 2021","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"16 October 2021","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"spe2021","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"http:\/\/www.spe2021.uevora.pt\/en\/inicio-english\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}