Single-index copulae

We introduce so-called "single-index copulae". They are semi-parametric conditional copulae whose parameter is an unknown "link" function of a univariate index only. We provide estimates of this link function and of the finite dimensional unknown parameter. The asymptotic properties of the latter estimates are stated. Thanks to some properties of conditional Kendall's tau, we illustrate our technical conditions with several usual copula families.

[1]  Andrew J. Patton.  Copula-Based Models for Financial Time Series , 2009 .

[2]  J. C. Rodríguez,et al.  Measuring financial contagion:a copula approach , 2007 .

[3]  Radu V. Craiu,et al.  Additive Models for Conditional Copulas , 2014 .

[4]  M. Delecroix,et al.  {$M$}-estimateurs semi-paramétriques dans les modèles à direction révélatrice unique , 1999 .

[5]  M. Rockinger,et al.  The Copula-GARCH model of conditional dependencies: An international stock market application , 2006 .

[6]  D. Pollard,et al.  $U$-Processes: Rates of Convergence , 1987 .

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

[8]  Radu V. Craiu,et al.  Statistical testing of covariate effects in conditional copula models , 2013 .

[9]  Jean-David Fermanian,et al.  About tests of the “simplifying” assumption for conditional copulas , 2016, 1612.07349.

[10]  R. Spady,et al.  AN EFFICIENT SEMIPARAMETRIC ESTIMATOR FOR BINARY RESPONSE MODELS , 1993 .

[11]  H. Tsukahara,et al.  Semiparametric estimation in copula models , 2005 .

[12]  Satishs Iyengar,et al.  Multivariate Models and Dependence Concepts , 1998 .

[13]  C. Genest,et al.  ESTIMATORS BASED ON KENDALL'S TAU IN MULTIVARIATE COPULA MODELS , 2011 .

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

[15]  Jon A. Wellner,et al.  Weak Convergence and Empirical Processes: With Applications to Statistics , 1996 .

[16]  H. Ichimura,et al.  SEMIPARAMETRIC LEAST SQUARES (SLS) AND WEIGHTED SLS ESTIMATION OF SINGLE-INDEX MODELS , 1993 .

[17]  Andrew J. Patton.  A review of copula models for economic time series , 2012, J. Multivar. Anal..

[18]  Radu V. Craiu,et al.  In mixed company: Bayesian inference for bivariate conditional copula models with discrete and continuous outcomes , 2012, J. Multivar. Anal..

[19]  D. W. Scott,et al.  Multivariate Density Estimation, Theory, Practice and Visualization , 1992 .

[20]  Thomas M. Stoker.  Consistent estimation of scaled coefficients , 2011 .

[21]  Thomas M. Stoker,et al.  Semiparametric Estimation of Index Coefficients , 1989 .

[22]  Uwe Einmahl,et al.  Uniform in bandwidth consistency of kernel-type function estimators , 2005 .

[23]  Radu V. Craiu,et al.  Dependence Calibration in Conditional Copulas: A Nonparametric Approach , 2011, Biometrics.

[24]  I. Keilegom,et al.  Single index regression models in the presence of censoring depending on the covariates , 2011, 1111.6232.

[25]  W. Härdle,et al.  Optimal Smoothing in Single-index Models , 1993 .

[26]  Friedrich Schmid,et al.  Multivariate Extensions of Spearman's Rho and Related Statistics , 2007 .

[27]  A. Frigessi,et al.  Pair-copula constructions of multiple dependence , 2009 .

[28]  P. Moran.  On the method of paired comparisons. , 1947, Biometrika.

[29]  W. Newey,et al.  Large sample estimation and hypothesis testing , 1986 .

[30]  Bill Ravens,et al.  An Introduction to Copulas , 2000, Technometrics.

[31]  Uwe Einmahl,et al.  An Empirical Process Approach to the Uniform Consistency of Kernel-Type Function Estimators , 2000 .

[32]  Christian Genest,et al.  Beyond simplified pair-copula constructions , 2012, J. Multivar. Anal..

[33]  Harry Joe,et al.  Multivariate concordance , 1990 .

[34]  Diego Dominici.  The Inverse of the Cumulative Standard Normal Probability Function , 2003 .

[35]  Andrew J. Patton.  Modelling Asymmetric Exchange Rate Dependence , 2006 .

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