Document Zbl 1077.62022

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J. Stat.</a> <a href="/?q=in%3A120727" title="Articles in this Issue">33, No. 3, 357-375 (2005)</a>; erratum ibid. 39, No. 4, 734 (2011). </div> <div class="abstract">Summary: The author recalls the limiting behaviour of the empirical copula process and applies it to prove some asymptotic properties of a minimum distance estimator for a Euclidian parameter in a copula model. The estimator in question is semiparametric in that no knowledge of the marginal distributions is necessary. The author also proposes another semiparametric estimator which he calls “rank approximate Z-estimator” and whose asymptotic normality he derives. He further presents Monte Carlo results for the comparison of various estimators in four well-known bivariate copula models.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=ci%3A2247280">Cited in <strong>1</strong> Review</a></div><div class="clear"><a href="/?q=rf%3A2247280">Cited in <strong>131</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A62G05" title="MSC2020">62G05</a> </td> <td class="space"> Nonparametric estimation </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A62G20" title="MSC2020">62G20</a> </td> <td class="space"> Asymptotic properties of nonparametric inference </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A65C05" title="MSC2020">65C05</a> </td> <td class="space"> Monte Carlo methods </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A62G30" title="MSC2020">62G30</a> </td> <td class="space"> Order statistics; empirical distribution functions </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Aasymptotic+distribution">asymptotic distribution</a>; <a href="/?q=ut%3Acopula+model">copula model</a>; <a href="/?q=ut%3Aempirical+copula">empirical copula</a>; <a href="/?q=ut%3Aminimum+distance+method">minimum distance method</a>; <a href="/?q=ut%3Arank">rank</a>; <a href="/?q=ut%3Asemiparametric+model">semiparametric model</a>; <a href="/?q=ut%3Asimulation">simulation</a>; <a href="/?q=ut%3AZ-estimator">Z-estimator</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1077.62022" data-ciurl="/ci/02247280" data-biburl="/bibtex/02247280.bib" data-amsurl="/amsrefs/02247280.bib" data-xmlurl="/xml/02247280.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/02247280.pdf" title="Zbl 1077.62022 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1002/cjs.5540330304" aria-label="DOI for “Semiparametric estimation in copula models”" title="10.1002/cjs.5540330304">DOI</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">M.Abramowitz & I. A.Stegun, eds. (1965). Handbook of Mathematical Functions. Dover, New York.</td> </tr><tr> <td>[2]</td> <td class="space">Beran, Handbook of Statistics, Volume 4: Nonparametric Methods pp 741– (1984) · <a href="/0547.62023" class="nowrap">Zbl 0547.62023</a></td> </tr><tr> <td>[3]</td> <td class="space">Bickel, Efficient and Adaptive Estimation for Semiparametric Models (1993) · <a href="/0786.62001" class="nowrap">Zbl 0786.62001</a></td> </tr><tr> <td>[4]</td> <td class="space">Cebrian, Testing for concordance ordering, Astin Bulletin 34 pp 151– (2004)</td> </tr><tr> <td>[5]</td> <td class="space">Clayton, A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence, Biometrika 65 pp 141– (1978) · <a href="/0394.92021" class="nowrap">Zbl 0394.92021</a></td> </tr><tr> <td>[6]</td> <td class="space">Dabrowska, Weak convergence of a product integral dependence measure, Scandinavian Journal of Statistics 23 pp 551– (1996) · <a href="/0907.62052" class="nowrap">Zbl 0907.62052</a></td> </tr><tr> <td>[7]</td> <td class="space">Dabrowska, Rank estimates in a class of semiparametric two-sample models, Annals of the Institute of Statistical Mathematics 41 pp 63– (1989) · <a href="/0723.62023" class="nowrap">Zbl 0723.62023</a></td> </tr><tr> <td>[8]</td> <td class="space">Deheuvels, La fonction de dépendance empirique et ses propriétés: un test non paramétrique d’indépendance, Académie royale de Belgique, Bulletin de la classe des sciences: 5e série 65 pp 274– (1979)</td> </tr><tr> <td>[9]</td> <td class="space">Donoho, The ”automatic” robustness of minimum distance functionals, The Annals of Statistics 16 pp 552– (1988) · <a href="/0684.62030" class="nowrap">Zbl 0684.62030</a></td> </tr><tr> <td>[10]</td> <td class="space">Drouet-Mari, Correlation and Dependence (2001) · <a href="https://doi.org/10.1142/p226" class="nowrap">doi:10.1142/p226</a></td> </tr><tr> <td>[11]</td> <td class="space">Dvoretzky, Asymptotic minimax character of the sample distribution function and of the classical multinomial estimator, The Annals of Mathematical Statistics 27 pp 642– (1956) · <a href="/0073.14603" class="nowrap">Zbl 0073.14603</a></td> </tr><tr> <td>[12]</td> <td class="space">Einmahl, Multivariate Empirical Processes (1987)</td> </tr><tr> <td>[13]</td> <td class="space">Embrechts, Risk Management: Value at Risk and Beyond pp 176– (2002) · <a href="https://doi.org/10.1017/CBO9780511615337.008" class="nowrap">doi:10.1017/CBO9780511615337.008</a></td> </tr><tr> <td>[14]</td> <td class="space">Fermanian, Weak convergence of empirical copula processes, Bernoulli 10 pp 847– (2004) · <a href="/1068.62059" class="nowrap">Zbl 1068.62059</a></td> </tr><tr> <td>[15]</td> <td class="space">J.-D. Fermanian & O. Scaillet (2004). Some statistical pitfalls in copula modeling for financial applications. HEC Genève: http://www.hec.unige.ch/recherches_publications/cahiers/2004/2004.02.pdf</td> </tr><tr> <td>[16]</td> <td class="space">Frees, Understanding relationships using copulas, North American Actuarial Journal 2 pp 1– (1998) · <a href="/1081.62564" class="nowrap">Zbl 1081.62564</a> · <a href="https://doi.org/10.1080/10920277.1998.10595667" class="nowrap">doi:10.1080/10920277.1998.10595667</a></td> </tr><tr> <td>[17]</td> <td class="space">Gänssler, Seminar on Empirical Processes (1987) · <a href="https://doi.org/10.1007/978-3-0348-6269-1" class="nowrap">doi:10.1007/978-3-0348-6269-1</a></td> </tr><tr> <td>[18]</td> <td class="space">Genest, Frank’s family of bivariate distributions, Biometrika 74 pp 549– (1987) · <a href="/0635.62038" class="nowrap">Zbl 0635.62038</a></td> </tr><tr> <td>[19]</td> <td class="space">Genest, A semiparametric estimation procedure of dependence parameters in multivariate families of distributions, Biometrika 82 pp 543– (1995) · <a href="/0831.62030" class="nowrap">Zbl 0831.62030</a></td> </tr><tr> <td>[20]</td> <td class="space">Genest, Distributions with Given Marginals and Statistical Modelling pp 103– (2002) · <a href="https://doi.org/10.1007/978-94-017-0061-0_12" class="nowrap">doi:10.1007/978-94-017-0061-0_12</a></td> </tr><tr> <td>[21]</td> <td class="space">Ghoudi, Asymptotic Methods in Stochastics: Festschrift for Miklós Csörg( pp 381– (2004) · <a href="https://doi.org/10.1090/fic/044/22" class="nowrap">doi:10.1090/fic/044/22</a></td> </tr><tr> <td>[22]</td> <td class="space">Glidden, A two-stage estimator of the dependence parameter for the Clayton-Oakes model, Lifetime Data Analysis 6 pp 141– (2000) · <a href="/1054.62113" class="nowrap">Zbl 1054.62113</a></td> </tr><tr> <td>[23]</td> <td class="space">Hougaard, Analysis of Multivariate Survival Data (2000) · <a href="/0962.62096" class="nowrap">Zbl 0962.62096</a> · <a href="https://doi.org/10.1007/978-1-4612-1304-8" class="nowrap">doi:10.1007/978-1-4612-1304-8</a></td> </tr><tr> <td>[24]</td> <td class="space">Joe, Multivariate Models and Dependence Concepts (1997) · <a href="/0990.62517" class="nowrap">Zbl 0990.62517</a> · <a href="https://doi.org/10.1201/b13150" class="nowrap">doi:10.1201/b13150</a></td> </tr><tr> <td>[25]</td> <td class="space">Kiefer, On large deviations of the empiric D. F. of vector chance variables and a law of iterated logarithm, Pacific Journal of Mathematics 11 pp 649– (1961) · <a href="/0119.34904" class="nowrap">Zbl 0119.34904</a> · <a href="https://doi.org/10.2140/pjm.1961.11.649" class="nowrap">doi:10.2140/pjm.1961.11.649</a></td> </tr><tr> <td>[26]</td> <td class="space">Kiefer, Nonparametric Techniques in Statistical Inference pp 299– (1970)</td> </tr><tr> <td>[27]</td> <td class="space">Klaassen, Efficient estimation in the bivariate normal copula model: normal margins are least-favorable, Bernoulli 3 pp 55– (1997) · <a href="/0877.62055" class="nowrap">Zbl 0877.62055</a></td> </tr><tr> <td>[28]</td> <td class="space">Maguluri, Semiparametric estimation of association in a bivariate survival function, The Annals of Statistics 21 pp 1648– (1993) · <a href="/0792.62027" class="nowrap">Zbl 0792.62027</a></td> </tr><tr> <td>[29]</td> <td class="space">Millar, Robust estimation via minimum distance methods, Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete 55 pp 73– (1981)</td> </tr><tr> <td>[30]</td> <td class="space">Millar, École d’été de probabilités de Saint-Flour XI-1981 pp 75– (1983)</td> </tr><tr> <td>[31]</td> <td class="space">Nelsen, An Introduction to Copulas (1999) · <a href="/0909.62052" class="nowrap">Zbl 0909.62052</a> · <a href="https://doi.org/10.1007/978-1-4757-3076-0" class="nowrap">doi:10.1007/978-1-4757-3076-0</a></td> </tr><tr> <td>[32]</td> <td class="space">Neuhaus, On weak convergence of stochastic processes with multidimensional time parameter, The Annals of Mathematical Statistics 42 pp 1285– (1971) · <a href="/0222.60013" class="nowrap">Zbl 0222.60013</a></td> </tr><tr> <td>[33]</td> <td class="space">Oakes, A model for association in bivariate survival data, Journal of the Royal Statistical Society Series B 44 pp 414– (1982) · <a href="/0503.62035" class="nowrap">Zbl 0503.62035</a></td> </tr><tr> <td>[34]</td> <td class="space">Ruymgaart, Asymptotic Theory of Rank Tests for Independence (1978)</td> </tr><tr> <td>[35]</td> <td class="space">Shih, Inferences on the association parameter in copula models for bivariate survival data, Biometrics 51 pp 1384– (1995) · <a href="/0869.62083" class="nowrap">Zbl 0869.62083</a></td> </tr><tr> <td>[36]</td> <td class="space">Sklar, Fonctions de répartition à n dimensions et leurs marges, Publications de I’Institut de statistique de l’Université de Paris 8 pp 229– (1959)</td> </tr><tr> <td>[37]</td> <td class="space">Stute, The oscillation behavior of empirical processes: the multivariate case, The Annals of Probability 12 pp 361– (1984) · <a href="/0533.62037" class="nowrap">Zbl 0533.62037</a></td> </tr><tr> <td>[38]</td> <td class="space">Tsukahara, A rank estimator in the two-sample transformation model with randomly censored data, Annals of the Institute of Statistical Mathematics 44 pp 313– (1992) · <a href="/0763.62017" class="nowrap">Zbl 0763.62017</a></td> </tr><tr> <td>[39]</td> <td class="space">H. Tsukahara (2000). Empirical Copulas and Some Applications. Research Report No 27, The Institute for Economic Studies, Seijo University: http://www.seijo.ac.jp/research/keiken/green/green27.pdf</td> </tr><tr> <td>[40]</td> <td class="space">van der Vaart, Weak Convergence and Empirical Processes: With Applications to Statistics (1996) · <a href="/0862.60002" class="nowrap">Zbl 0862.60002</a> · <a href="https://doi.org/10.1007/978-1-4757-2545-2" class="nowrap">doi:10.1007/978-1-4757-2545-2</a></td> </tr><tr> <td>[41]</td> <td class="space">Wang, On assessing the association for bivariate current status data, Biometrika 87 pp 879– (2000) · <a href="/1028.62077" class="nowrap">Zbl 1028.62077</a></td> </tr></table> <div class="reference_disclaimer"> 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. 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