Related papers: Ordinal pattern dependence as a multivariate depen…
We present a framework for selecting and developing measures of dependence when the goal is the quantification of a relationship between two variables, not simply the establishment of its existence. Much of the literature on dependence…
Two families of dependence measures between random variables are introduced. They are based on the R\'enyi divergence of order $\alpha$ and the relative $\alpha$-entropy, respectively, and both dependence measures reduce to Shannon's mutual…
Test of independence plays a fundamental role in many statistical techniques. Among the nonparametric approaches, the distance-based methods (such as the distance correlation based hypotheses testing for independence) have numerous…
In this paper we obtain advances for the concept of directional $\rho$-coefficients, originally defined for the trivariate case in [Nelsen, R.B., \'Ubeda-Flores, M. (2011). Directional dependence in multivariate distributions. Ann. Inst.…
Ordinal regression (OR, also called ordinal classification) is classification of ordinal data, in which the underlying target variable is categorical and considered to have a natural ordinal relation for the underlying explanatory variable.…
In this paper we examine rigorously the evidence for dependence among data size, transfer rate and duration in Internet flows. We emphasize two statistical approaches for studying dependence, including Pearson's correlation coefficient and…
Davis and Mikosch [7] introduced the extremogram as a flexible quantitative tool for measuring various types of extremal dependence in a stationary time series. There we showed some standard statistical properties of the sample extremogram.…
This article proposes a generalized notion of extreme multivariate dependence between two random vectors which relies on the extremality of the cross-covariance matrix between these two vectors. Using a partial ordering on the…
Multivariate time series data that capture the temporal evolution of interconnected systems are ubiquitous in diverse areas. Understanding the complex relationships and potential dependencies among co-observed variables is crucial for the…
We establish a definition of ordinal patterns for multivariate data sets based on the concept of Tukey's halfspace depth. Given the definition of these \emph{depth patterns}, we are interested in the probabilities of observing specific…
We consider quantum systems with a chaotic classical limit that depend on an external parameter, and study correlations between the spectra at different parameter values. In particular, we consider the parametric spectral form factor…
In this paper, we study dependence uncertainty and the resulting effects on tail risk measures, which play a fundamental role in modern risk management. We introduce the notion of a regular dependence measure, defined on multi-marginal…
Independence testing plays a central role in statistical and causal inference from observational data. Standard independence tests assume that the data samples are independent and identically distributed (i.i.d.) but that assumption is…
Regular variation provides a convenient theoretical framework to study large events. In the multivariate setting, the dependence structure of the positive extremes is characterized by a measure - the spectral measure - defined on the…
We analyze the extreme value dependence of independent, not necessarily identically distributed multivariate regularly varying random vectors. More specifically, we propose estimators of the spectral measure locally at some time point and…
Detecting dependence between two random variables is a fundamental problem. Although the Pearson correlation is effective for capturing linear dependency, it can be entirely powerless for detecting nonlinear and/or heteroscedastic patterns.…
We present a general central limit theorem with simple, easy-to-check covariance-based sufficient conditions for triangular arrays of random vectors when all variables could be interdependent. The result is constructed from Stein's method,…
Due to globalization and relaxed market regulation, we have assisted to an increasing of extremal dependence in international markets. As a consequence, several measures of tail dependence have been stated in literature in recent years,…
This paper extends the class of ordinal regression models with a structured interpretation of the problem by applying a novel treatment of encoded labels. The net effect of this is to transform the underlying problem from an ordinal…
The Pearson correlation coefficient is commonly used for quantifying the global level of degree-degree association in complex networks. Here, we use a probabilistic representation of the underlying network structure for assessing the…