The analysis of the copula as a semantically vacuous word in mainstream HPSG is appropriate for some of its uses, such as the progressive and the passive, but not for its use in clauses with a predicate complement. In such clauses the copula denotes a relation of coreference between the indices of the subject and the predicate complement. 1 The Fregean treatment In HPSG the copula is commonly t...

Copula has become a standard tool in describing dependent relations between random variables. This paper proposes a nonparametric bivariate copula estimation method based on shape-restricted -support vector regression ( -SVR). This method explicitly supplements the classical -SVR with constraints related to three shape restrictions: grounded, marginal and 2-increasing, which are the necessary a...

Consider semiparametric bivariate copula models in which the family of copula functions is parametrized by a Euclidean parameter θ of interest and in which the two unknown marginal distributions are the (infinite dimensional) nuisance parameters. The efficient score for θ can be characterized in terms of the solutions of two coupled Sturm-Liouville equations. In case the family of copula functi...

We investigate the dynamic and asymmetric dependence structure between equity portfolios from the US and UK. We demonstrate the statistical significance of dynamic asymmetric copula models in modelling and forecasting market risk. First, we construct “high-minus-low" equity portfolios sorted on beta, coskewness, and cokurtosis. We find substantial evidence of dynamic and asymmetric dependence b...

We give a purely probabilistic proof of Sklar’s theorem by a simple continuing technique and sequential arguments. We then consider the case where the distribution function F is unknown but one observes instead a sample of i.i.d. copies distributed from F : we construct a sequence of copula representers associated to the empirical distribution function of the sample which convergences a.s. to t...

A pair-copula construction is a decomposition of a multivariate copula into a structured system, called regular vine, of bivariate copulae or pair-copulae. The standard practice is to model these pair-copulae parametri-cally, which comes at the cost of a large model risk, with errors propagating throughout the vine structure. The empirical pair-copula proposed in the paper provides a nonparamet...

Recently, several copula-based approaches have been proposed for modeling stationary multivariate time series. All of them are based on vine copulas, and they differ in the choice of the regular vine structure. In this article, we consider a copula autoregressive (COPAR) approach to model the dependence of unobserved multivariate factors resulting from two dynamic factor models. However, the pr...

We study estimation and model selection of semiparametric models of multivariate survival functions for censored data, which are characterized by possibly misspecified parametric copulas and nonparametric marginal survivals. We obtain the consistency and root-n asymptotic normality of a two-step copula estimator to the pseudo-true copula parameter value according to KLIC, and provide a simple c...

We propose a CUSUM type test for constant correlation that goes beyond a previously suggested correlation constancy test by considering Spearman’s rho in arbitrary dimensions. By using copula-based expressions, we simultaneously extend a previously suggested copula constancy test. We calculate the asymptotic null distribution using an invariance principle for the sequential empirical copula pro...

On the basis of order statistics, Baker (2008) proposed a method for constructing multivariate distributions with fixed marginals. This is another representation of the Bernstein copula. According to the construction of Baker’s distribution, the Bernstein copula can be regarded as a finite mixture distribution. In this paper, we propose expectationmaximization (EM) algorithms to estimate the Be...