Related papers: Nonparametric Universal Copula Modeling
Functional graphical models have undergone extensive development during the recent years, leading to a variety models such as the functional Gaussian graphical model, the functional copula Gaussian graphical model, the functional Bayesian…
Most data is multi-dimensional. Discovering whether any subset of dimensions, or subspaces, of such data is significantly correlated is a core task in data mining. To do so, we require a measure that quantifies how correlated a subspace is.…
Using a characterization of Mutual Complete Dependence copulas, we show that, with respect to the Sobolev norm, the MCD copulas can be approximated arbitrarily closed by shuffles of Min. This result is then used to obtain a characterization…
The majority of model-based clustering techniques is based on multivariate Normal models and their variants. In this paper copulas are used for the construction of flexible families of models for clustering applications. The use of copulas…
The probabilistic characterization of the relationship between two or more random variables calls for a notion of dependence. Dependence modeling leads to mathematical and statistical challenges, and recent developments in extremal…
In many applications including financial risk measurement, copulas have shown to be a powerful building block to reflect multivariate dependence between several random variables including the mapping of tail dependencies. A famous key…
Quantitative studies in many fields involve the analysis of multivariate data of diverse types, including measurements that we may consider binary, ordinal and continuous. One approach to the analysis of such mixed data is to use a copula…
Multivariate functions emerge naturally in a wide variety of data-driven models. Popular choices are expressions in the form of basis expansions or neural networks. While highly effective, the resulting functions tend to be hard to…
Using the classical estimation method of moments, we propose a new semiparametric estimation procedure for multi-parameter copula models. Consistency and asymptotic normality of the obtained estimators are established. By considering an…
The exclusive or (xor) function is one of the simplest examples that illustrate why nonlinear feedforward networks are superior to linear regression for machine learning applications. We review the xor representation and approximation…
An overview of existing nonparametric tests of extreme-value dependence is presented. Given an i.i.d.\ sample of random vectors from a continuous distribution, such tests aim at assessing whether the underlying unknown copula is of the {\em…
The empirical copula process, a fundamental tool for copula inference, is studied in the high dimensional regime where the dimension is allowed to grow to infinity exponentially in the sample size. Under natural, weak smoothness assumptions…
We introduce a novel bivariate copula model able to capture both the central and tail dependence of the joint probability distribution. Model that can capture the dependence structure within the joint tail have important implications in…
The thesis is composed of three parts. Part I introduces the mathematical and statistical tools that are relevant for the study of dependences, as well as statistical tests of Goodness-of-fit for empirical probability distributions. I…
This is a gentle introduction to Colombeau nonlinear generalized functions, a generalization of the concept of distributions such that distributions can freely be multiplied. It is intended to physicists and applied mathematicians who…
We introduce a new family of copula densities constructed from univariate distributions on $[0,1]$. Although our construction is structurally simple, the resulting family is versatile: it includes both smooth and irregular examples, and…
We propose a comprehensive Bayesian approach for graphical model determination in observational studies that can accommodate binary, ordinal or continuous variables simultaneously. Our new models are called copula Gaussian graphical models…
We propose a framework for determining whether the causal dependence of an outcome $Y$ on a covariate $X$ changes at a given time point, given confounders $\boldsymbol{Z}$. For instance, in financial markets, the effect of a market…
We investigate in multidimensional compound Poisson processes (CPP) the relation between the dependence structure of the jump distribution and the dependence structure of the respective components of the CPP itself. For this purpose the…
Parametric copula families have been known to flexibly capture various dependence patterns, e.g., either positive or negative dependence in either the lower or upper tails of bivariate distributions. In this paper, our objective is to…