Related papers: Directional $\rho$-coefficients
Rank-based dependence measures such as Spearman's footrule are robust and invariant, but they often fail to capture directional or asymmetric dependence in multivariate settings. This paper introduces a new family of directional Spearman's…
Codifferentials and coexhausters are used to describe nonhomogeneous approximations of a nonsmooth function. Despite the fact that coexhausters are modern generalizations of codifferentials, the theories of these two concepts continue to…
In this paper we introduce a notion of a directional uncertainty product for multivariate periodic functions. It measures a localization of a function along a particular direction. We study properties of the uncertainty product and give an…
We introduce an operator-theoretic framework for analyzing directional dependence in multivariate time series based on order-constrained spectral non-invariance. Directional influence is defined as the sensitivity of second-order dependence…
Distance multivariance is a multivariate dependence measure, which can detect dependencies between an arbitrary number of random vectors each of which can have a distinct dimension. Here we discuss several new aspects, present a concise…
Thanks to its favorable properties, the multivariate normal distribution is still largely employed for modeling phenomena in various scientific fields. However, when the number of components $p$ is of the same asymptotic order as the sample…
We introduce, and analyze, three measures for degree-degree dependencies, also called degree assortativity, in directed random graphs, based on Spearman's rho and Kendall's tau. We proof statistical consistency of these measures in general…
Projected distributions have proved to be useful in the study of circular and directional data. Although any multivariate distribution can be used to produce a projected model, these distributions are typically parametric. In this article…
A popular measure of association is the tail dependence coefficient which measures the strength of dependence in either the lower-left or upper-right tail of a bivariate distribution. In this paper, we develop the idea of quantile…
Situations of a functional predictor paired with a scalar response are increasingly encountered in data analysis. Predictors are often appropriately modeled as square integrable smooth random functions. Imposing minimal assumptions on the…
Directional data consists of unit vectors in q-dimensions that can be described in polar or Cartesian coordinates. Axial data can be viewed as a pair of directions pointed in opposite directions or as a projection matrix of rank 1.…
We consider the problem of estimating the mean of a random vector based on $N$ independent, identically distributed observations. We prove the existence of an estimator that has a near-optimal error in all directions in which the variance…
We introduce some new indexes to measure the departure of any multivariate continuous distribution on non-negative orthant from a given reference one such the uncorrelated exponential model, similar to the relative Fisher dispersion indexes…
Motivated by extending the functional stochastic calculus, to important functionals to which it does not apply, a notion of functional derivative along a curve is introduced. This new setting is developed by incorporating path-dependent…
Pearson's $\rho$ is the most used measure of statistical dependence. It gives a complete characterization of dependence in the Gaussian case, and it also works well in some non-Gaussian situations. It is well known, however, that it has a…
In physics, density $\rho(\cdot)$ is a fundamentally important scalar function to model, since it describes a scalar field or a probability density function that governs a physical process. Modeling $\rho(\cdot)$ typically scales poorly…
The need to test whether two random vectors are independent has spawned a large number of competing measures of dependence. We are interested in nonparametric measures that are invariant under strictly increasing transformations, such as…
In a recent article, we showed that trigonometric shearlets are able to detect directional step discontinuities along edges of periodic characteristic functions. In this paper, we extend these results to multivariate periodic functions…
Many physical and mathematical models involve random fields in their input data. Examples are ordinary differential equations, partial differential equations and integro--differential equations with uncertainties in the coefficient…
This paper discusses a design-dependent nature of variance in nonparametric link regression aiming at predicting a mean outcome at a link, i.e., a pair of nodes, based on currently observed data comprising covariates at nodes and outcomes…