Nonparametric estimation of the conditional tail copula

The tail copula is widely used to describe the dependence in the tail of multivariate distributions. In some situations such as risk management, the dependence structure may be linked with some covariate. The tail copula thus depends on this covariate and is referred to as the conditional tail copula. The aim of this paper is to propose a nonparametric estimator of the conditional tail copula and to establish its asymptotic normality. Some illustrations are presented both on simulated and real datasets.

[1]  I. Gijbels,et al.  Multivariate and functional covariates and conditional copulas , 2012 .

[2]  Paul Deheuvels,et al.  On the limiting behavior of the Pickands estimator for bivariate extreme-value distributions , 1991 .

[3]  T. Ané,et al.  Dependence Structure and Risk Measure , 2003 .

[4]  M. Meerschaert.  Regular Variation in R k , 1988 .

[5]  I. Gijbels,et al.  Estimation of a Conditional Copula and Association Measures , 2011 .

[6]  U. Stadtmüller,et al.  Generalized regular variation of second order , 1996, Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics.

[7]  Liang Peng,et al.  Nonparametric estimation of the dependence function for a multivariate extreme value distribution , 2008 .

[8]  C. Genest,et al.  Bivariate Distributions with Given Extreme Value Attractor , 2000 .

[9]  L. Haan,et al.  Extreme value theory : an introduction , 2006 .

[10]  J. Segers.  Asymptotics of empirical copula processes under non-restrictive smoothness assumptions , 2010, 1012.2133.

[11]  Christian Genest,et al.  A nonparametric estimation procedure for bivariate extreme value copulas , 1997 .

[12]  Masaaki Sibuya,et al.  Bivariate extreme statistics, I , 1960 .

[13]  Irène Gijbels,et al.  Semiparametric estimation of conditional copulas , 2012, J. Multivar. Anal..

[14]  M. Sklar.  Fonctions de repartition a n dimensions et leurs marges , 1959 .

[15]  L. Haan,et al.  Parametric tail copula estimation and model testing , 2008 .

[16]  S. Chen,et al.  Nonparametric estimation of copula functions for dependence modelling , 2007 .

[17]  S. Girard,et al.  Kernel estimators of extreme level curves , 2011 .

[18]  Christian Genest,et al.  Using B-splines for nonparametric inference on bivariate extreme-value copulas , 2014 .

[19]  J. De Gooijer,et al.  On the U-Th Geometric Conditional Quantile , 2004 .

[20]  Johan Segers,et al.  Nonparametric estimation of an extreme-value copula in arbitrary dimensions , 2009, J. Multivar. Anal..

[21]  S. Girard,et al.  Functional kernel estimators of large conditional quantiles , 2011, 1107.2261.

[22]  Aristidis K. Nikoloulopoulos,et al.  Tail dependence functions and vine copulas , 2010, J. Multivar. Anal..

[23]  E. Seneta,et al.  Modelling and Estimation for Bivariate Financial Returns , 2010 .

[24]  Irène Gijbels,et al.  Conditional copulas, association measures and their applications , 2011, Comput. Stat. Data Anal..

[25]  S. Girard,et al.  On kernel smoothing for extremal quantile regression , 2012, 1312.5123.

[26]  Projection estimators of Pickands dependence functions , 2008 .

[27]  Thomas M. Stoker,et al.  Investigating Smooth Multiple Regression by the Method of Average Derivatives , 2015 .

[28]  J. Segers,et al.  RANK-BASED INFERENCE FOR BIVARIATE EXTREME-VALUE COPULAS , 2007, 0707.4098.

[29]  J. Mielniczuk,et al.  Estimating the density of a copula function , 1990 .

[30]  Lei Si Ni Ke Resnick.S.I..  Extreme values. regular variation. and point processes , 2011 .

[31]  P. Embrechts,et al.  Quantitative Risk Management: Concepts, Techniques, and Tools , 2005 .

[32]  Nicole A. Lazar,et al.  Statistics of Extremes: Theory and Applications , 2005, Technometrics.

[33]  Brahim Brahimi.  Statistics of Bivariate Extreme Values , 2014 .

[34]  Léo R. Belzile,et al.  Multivariate Extreme Value Distributions , 2015 .

[35]  Hansheng Wang,et al.  A note on tail dependence regression , 2013, J. Multivar. Anal..

[36]  P. Hall,et al.  Distribution and dependence-function estimation for bivariate extreme-value distributions , 2000 .

[37]  E. Parzen.  On Estimation of a Probability Density Function and Mode , 1962 .

[38]  Goodness-of-fit test for tail copulas modeled by elliptical copulas , 2009 .

[39]  S. Resnick.  Extreme Values, Regular Variation, and Point Processes , 1987 .

[40]  Johan Segers,et al.  Nonparametric estimation of multivariate extreme-value copulas , 2011, 1107.2410.

[41]  Rafael Schmidt,et al.  Non‐parametric Estimation of Tail Dependence , 2006 .

[42]  Modelling dependence of extreme events in energy markets using tail copulas , 2012 .