A copula is best described, as in Joe (1997), as a multivariate distribution function that is used to bind each marginal distribution function to form the joint. The copula parameterises the dependence between the margins, while the parameters of each marginal distribution function can be estimated separately. This is a brief introduction to copulas and multivariate dependence issues within a h...

Abstract: In conditional copula models, the copula parameter is deterministically linked to a covariate via the calibration function. The latter is of central interest for inference and is usually estimated nonparametrically. However, in many applications it is scientifically important to test whether the calibration function is constant or not. Moreover, a correct model of a constant relations...

The entropy theory has been widely applied in hydrology for probability inference based on incomplete information and the principle of maximum entropy. Meanwhile, copulas have been extensively used for multivariate analysis and modeling the dependence structure between hydrologic and climatic variables. The underlying assumption of the principle of maximum entropy is that the entropy variables ...

Parametric conditional copulamodels allow the copula parameters to vary with a set of covariates according to an unknown calibration function. Flexible Bayesian inference for the calibration function of a bivariate conditional copula is introduced. The prior distribution over the set of smooth calibration functions is built using a sparse Gaussian process (GP) prior for the single index model (...

Kernel-based Copula Processes Eddie K. H. Ng Doctor of Philosophy Graduate Department of Electrical & Computer Engineering University of Toronto 2010 The field of time-series analysis has made important contributions to a wide spectrum of applications such as tide-level studies in hydrology, natural resource prospecting in geo-statistics, speech recognition, weather forecasting, financial tradi...

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...

A copula-based method to integrate a real vector-valued function, obtaining a single real number, is discussed. Special attention is paid to the case when the underlying universe is finite. The integral considered here is shown to be an extension of [0, 1]-valued copula-based universal integrals.

Based on the asymmetric copula function, this paper analyzes static and dynamic correlation between Shanghai Composite Index Shenzhen Index. Through analysis, it is found that function better than Gumbel Copula in describing distribution characteristics of top tail dependence Index, coefficient definition based can well describe variables. In time-varying improves traditional evolution equation...

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...