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We establish in this paper the uniform-in-bandwidth consistency for general kernel-type estimators of regression. More precisely, we investigate the regression estimator based on copula representation. The asymptotic properties are driven by a U -statistic relying on the methods developed in Dony and Mason (2008). [ABSTRACT FROM AUTHOR]

In this paper, we establish the second-order distributional expansions of normalized maxima of n independent observations, where the i th observation follows from a normal copula with its correlation coefficient being a monotone continuous function. These expansions can be used to deduce the convergence rates of distributions of normalized maxima to their limits. [ABSTRACT FROM AUTHOR]

We revisit the notion of Conditional Value-at-Risk (shortly, CoVaR) by weakening the usual assumptions on the joint distribution function of the involved random variables. The new approach exploits the copula methodology and uses the concept of Dini derivatives. A directory of CoVaR values for different families of copulas is provided. [ABSTRACT FROM AUTHOR]

We study the problem of how to transform a copula for the distribution function of an arbitrary random vector into a copula for the distribution function of its order statistic. We thus extend results of Navarro and Spizzichino (2010). [ABSTRACT FROM AUTHOR]

A new property defined on the class of symmetric copulas is introduced and studied along this note. It is shown here that such a property can define a family of bivariate distribution functions satisfying all the characteristics listed in Kimeldorf and Sampson (1989) to be considered as a positive dependence notion. Applications, relationships with other positive dependence notions, further properties and the corresponding negative dependence notion are discussed as well. [ABSTRACT FROM AUTHOR]

We consider the tail behavior of the conditional tail expectation E ( S n θ ∣ S n θ > x q ) when q ↑ 1 . Here S n θ = ∑ i = 1 n θ i X i and x q = VaR q ( S n θ ) = inf { y ∈ R : P ( S n θ ⩽ y ) ⩾ q } . We are interested in the case when the primary random variables X 1 , X 2 , … , X n are real-valued and regularly varying, while the random weights θ 1 , θ 2 , … , θ n are nonnegative and not degenerate at zero. We suppose that random vectors ( X 1 , θ 1 ) , ( X 2 , θ 2 ) , … ( X n , θ n ) are independent, while X k and θ k follow a certain dependence structure. We also present the related asymptotic results, some of which hold if distribution functions of X 1 , X 2 , … , X n are long tailed and dominatingly varying. [ABSTRACT FROM AUTHOR]

Akaike Information Criterion (AIC) is frequently employed in the semiparametric setting of selection of copula models, even though as a model selection tool it was developed in a parametric setting. Recently a Copula Information Criterion (CIC) has been especially designed for copula model selection. In this paper we examine the two approaches and present a simulation study where the performance of a cross-validated version of CIC is compared with the AIC criterion. Only minor differences are observed. [ABSTRACT FROM AUTHOR]

Abstract: We study two-dimensional self-similar Ito diffusions whose margins are Wiener processes. We characterize the copulas of the random pairs for a given . [Copyright &y& Elsevier]

Abstract: We derive the joint distribution of the ranks associated with a given bivariate random sample. Using these results, exact non-asymptotic expressions and asymptotic expansions for the mean and variance of the classical empirical copula estimator are obtained. An explicit expression of the coefficient appearing in the -term for the mean can, for example, be found; a result that apparently does not appear in the existing literature. Furthermore, it is shown that similar explicit non-asymptotic expressions as well as asymptotic expansions can be derived for the rank-based Bernstein copula estimator. [Copyright &y& Elsevier]

Abstract: In this work, we derive a sufficient condition for the orthant convex order based on the single crossing of the respective joint survival functions. This condition is expressed in terms of the generators for Archimedean copulas. Numerical examples show that this condition is valid for members of standard copula families (including the Clayton and Frank ones). [Copyright &y& Elsevier]

Abstract: In his paper ▪A probabilistic interpretation of complete monotonicity ▪  proves several remarkable results connecting multivariate distribution functions and their marginals via completely monotone functions on the half-line. These have been taken up more recently in particular in connection with so-called Archimedean copulas; see for example . We present in this paper much shorter proofs of more general versions of the two main theorems in , and apply this to show the max-infinite divisibility of some known Archimedean copulas. [ABSTRACT FROM AUTHOR]

Abstract: It is well known that the empirical copula process converges weakly to a centered Gaussian field. Because the covariance structure of the limiting process depends on the partial derivatives of the unknown copula several bootstrap approximations for the empirical copula process have been proposed in the literature. We present a brief review of these procedures. Because some of these procedures also require the estimation of the derivatives of the unknown copula we propose an alternative approach which circumvents this problem. Finally a simulation study is presented in order to compare the different bootstrap approximations for the empirical copula process. [ABSTRACT FROM AUTHOR]

Abstract: We present and study a method for constructing multivariate copulas, which includes both the shuffles of Min and the ordinal sums. Such a method has been used in order to show that suitable transformations of a given copula constitute a dense set in the class of all copulas with respect to the norm. [ABSTRACT FROM AUTHOR]

Abstract: Modeling and estimating a tail copula play an important role in forecasting rare events. Due to their easy simulation, elliptical copulas have been employed in risk management. Recently, Klüppelberg, [Klüppelber, C., Kuhn, G., Peng, L., 2007. Estimating the tail dependence function of an elliptical distribution. Bernoulli 13 (1), 229–251; Klüppelberg, C., Kuhn, G., Peng, L., 2008. Semi-parametric models for the multivariate tail dependence function—the asymptotically dependent case. Scandinavian Journal of Statistics 35, 701–718] proposed to model a tail copula by an elliptical copula, which results in an explicit parametric model for the tail copula. In this paper, we propose a goodness-of-fit test for such a parametric model and some real data analyses show that this fitting cannot be rejected. Therefore we demonstrate the practical applicability of this model. [Copyright &y& Elsevier]

Abstract: Starting with a notion of positive dependence and with the family of the lower threshold copulas associated with a bivariate distribution having copula , we define different notions of positive dependence for , reflecting the dependence properties of the copulas for some . Then, we analyze some structural aspects of lower threshold copulas and of the given definitions. Furthermore we consider several specific cases arising from relevant special choices of (e.g., PQD, LTD, TP and PLR). Our analysis, in particular, allows us to present a number of relevant examples and counter-examples, which can be useful in the study of the tail dependence for a bivariate distribution. [Copyright &y& Elsevier]

Abstract: In this paper we discuss the properties of the orderings of positive dependence introduced by Hollander et al. [Hollander, M., Proschan, F., Sconing, J., 1990. Information, censoring, and dependence. In: Topics in Statistical Dependence (Somerset, PA, 1987). In: IMS Lecture Notes Monogr. Ser., vol. 16. pp. 257–268. Inst. Math. Statist., Hayward, CA] as generalizations of the bivariate positive dependence concepts of left-tail decreasing (LTD) and right-tail increasing (RTI) random vectors studied by Esary and Proschan [Esary, J.D., Proschan, F., 1972. Relationships among some concepts of bivariate dependence. Ann. Math. Statist. 43, 651–655]. We show which of the postulates proposed by Kimeldorf and Sampson [Kimeldorf, G., Sampson, A.R., 1987. Positive dependence orderings. Ann. Inst. Statist. Math. 39 (1), 113–128] for a reasonable positive dependence ordering are satisfied and how the orders can be studied by restricting them to copulas. We also investigate the relationships of these orders with some other orderings which have appeared in the literature and generalize the same notions of positive dependence. Finally, some applications to extreme value bivariate distributions are discussed. [Copyright &y& Elsevier]

Abstract: Convergence of a sequence of bivariate Archimedean copulas to another Archimedean copula or to the comonotone copula is shown to be equivalent with convergence of the corresponding sequence of Kendall distribution functions. No extra differentiability conditions on the generators are needed. [Copyright &y& Elsevier]

We study a wide class of bivariate copulas depending on two univariate functions which generalizes many known families of copulas. We measure the dependence of any copula of this class in different ways, exhibit several properties concerning symmetry, dependence concepts, and concordance ordering, and provide several examples. [Copyright &y& Elsevier]

A new class of bivariate distributions is constructed from a given family of distributions. The approach is based on the corresponding exponential representation, which generalizes the well-known exponential representation for the univariate survival function. [Copyright &y& Elsevier]

Square tray distributions have been studied by Johson and Kotz (Statist. Probab. Lett. 42 (1999) 157). As an extension, multiple square tray distributions are considered in this paper. These distributions are simple in the sense that there are only three different levels of the probability density function; they lead, however, to more complicated and revealing formulae for measures of dependence. [Copyright &y& Elsevier]