We study nonparametric estimators of conditional Kendall's tau, a measure of concordance between two random variables given some covariates. We prove non-asymptotic pointwise and uniform bounds, that hold with high probabilities. We provide "direct proofs" of the consistency and the asymptotic law of conditional Kendall's tau. A simulation study evaluates the numerical performance of such nonparametric estimators. An application to the dependence between energy consumption and temperature conditionally to calendar days is finally provided.@en

Several procedures have been recently proposed to test the simplifying assumption for conditional copulas. Instead of considering pointwise conditioning events, we study the constancy of the conditional dependence structure when some covariates belong to general Borel conditioning subsets. We introduce several test statistics based on the equality of conditional Kendall's taus and derive their asymptotic distributions under the null hypothesis. In settings where such conditioning events are not fixed ex ante, we propose a data-driven procedure to recursively build such relevant subsets. This procedure is based on decision trees that maximize the differences between the conditional Kendall's taus, which correspond to the leaves of the trees. Empirical results for such tests are illustrated in the Supplementary Material. Moreover, a study of the conditional dependence between financial stock returns is presented and highlights specific contagion effects of past returns. The last application deals with conditional dependence between coverage amounts in an insurance dataset.@en

This article deals with robust inference for parametric copula models. Estimation using canonical maximum likelihood might be unstable, especially in the presence of outliers. We propose to use a procedure based on the maximum mean discrepancy (MMD) principle. We derive nonasymptotic oracle inequalities, consistency and asymptotic normality of this new estimator. In particular, the oracle inequality holds without any assumption on the copula family, and can be applied in the presence of outliers or under misspecification. Moreover, in our MMD framework, the statistical inference of copula models for which there exists no density with respect to the Lebesgue measure on (Formula presented.), as the Marshall-Olkin copula, becomes feasible. A simulation study shows the robustness of our new procedures, especially compared to pseudo-maximum likelihood estimation. An R package implementing the MMD estimator for copula models is available. Supplementary materials for this article are available online.@en

We study the weak convergence of conditional empirical copula processes indexed by general families of conditioning events that have non zero probabilities. Moreover, we also study the case where the conditioning events are chosen in a data-driven way. The validity of several bootstrap schemes is stated, including the exchangeable bootstrap. We define general multivariate measures of association, possibly given some fixed or random conditioning events. By applying our theoretical results, we prove the asymptotic normality of the estimators of such measures. We illustrate our results with financial data.@en

Meta-elliptical copulas are often proposed to model dependence between the components of a random vector. They are specified by a correlation matrix and a map g, called density generator. While the latter correlation matrix can easily be estimated from pseudo-samples of observations, the density generator is harder to estimate, especially when it does not belong to a parametric family. We give sufficient conditions to non-parametrically identify this generator. Several nonparametric estimators of g are then proposed, by M-estimation, simulation-based inference, or by an iterative procedure available in the R package ElliptCopulas. Some simulations illustrate the relevance of the latter method.@en

It is shown how the problem of estimating conditional Kendall's tau can be rewritten as a classification task. Conditional Kendall's tau is a conditional dependence parameter that is a characteristic of a given pair of random variables. The goal is to predict whether the pair is concordant (value of 1) or discordant (value of −1) conditionally on some covariates. The consistency and the asymptotic normality of a family of penalized approximate maximum likelihood estimators is proven, including the equivalent of the logit and probit regressions in our framework. Specific algorithms are detailed, adapting usual machine learning techniques, including nearest neighbors, decision trees, random forests and neural networks, to the setting of the estimation of conditional Kendall's tau. Finite sample properties of these estimators and their sensitivities to each component of the data-generating process are assessed in a simulation study. Finally, all these estimators are applied to a dataset of European stock indices.@en

Conditional Kendall's tau is a measure of dependence between two random variables, conditionally on some covariates. We assume a regression-type relationship between conditional Kendall's tau and some covariates, in a parametric setting with a large number of transformations of a small number of regressors. This model may be sparse, and the underlying parameter is estimated through a penalized criterion and a two-step inference procedure. We prove non-asymptotic bounds with explicit constants that hold with high probabilities. We derive the consistency of the latter estimator, its asymptotic law and some oracle properties. Some simulations and applications to real data conclude the paper.@en

We discuss the so-called "simplifying assumption" of conditional copulas in a general framework. We introduce several tests of the latter assumption for non- and semiparametric copula models. Some related test procedures based on conditioning subsets instead of point-wise events are proposed. The limiting distributions of such test statistics under the null are approximated by several bootstrap schemes, most of them being new. We prove the validity of a particular semiparametric bootstrap scheme. Some simulations illustrate the relevance of our results.@en