Related papers: A fast algorithm for computing distance correlatio…
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…
The product moment covariance is a cornerstone of multivariate data analysis, from which one can derive correlations, principal components, Mahalanobis distances and many other results. Unfortunately the product moment covariance and the…
The "maximum similarity correlation" definition introduced in this study is motivated by the seminal work of Szekely et al on "distance covariance" (Ann. Statist. 2007, 35: 2769-2794; Ann. Appl. Stat. 2009, 3: 1236-1265). Instead of using…
To quantify the dependence between two random vectors of possibly different dimensions, we propose to rely on the properties of the 2-Wasserstein distance. We first propose two coefficients that are based on the Wasserstein distance between…
Application of the minimum distance method to the linear regression model for estimating regression parameters is a difficult and time-consuming process due to the complexity of its distance function, and hence, it is computationally…
We study the problem of estimating the covariance matrix of a high-dimensional distribution when a small constant fraction of the samples can be arbitrarily corrupted. Recent work gave the first polynomial time algorithms for this problem…
The most popular ways to test for independence of two ordinal random variables are by means of Kendall's tau and Spearman's rho. However, such tests are not consistent, only having power for alternatives with ``monotonic'' association. In…
We apply the concept of distance covariance for testing independence of two long-range dependent time series. As test statistic we propose a linear combination of empirical distance cross-covariances. We derive the asymptotic distribution…
Simple correlation coefficients between two variables have been generalized to measure association between two matrices in many ways. Coefficients such as the RV coefficient, the distance covariance (dCov) coefficient and kernel based…
In an extension of Kendall's $\tau$, Bergsma and Dassios (2014) introduced a covariance measure $\tau^*$ for two ordinal random variables that vanishes if and only if the two variables are independent. For a sample of size $n$, a direct…
Relying on recent advances in statistical estimation of covariance distances based on random matrix theory, this article proposes an improved covariance and precision matrix estimation for a wide family of metrics. The method is shown to…
We present a method for fast evaluation of the covariance matrix for a two-point galaxy correlation function (2PCF) measured with the Landy-Szalay estimator. The standard way of evaluating the covariance matrix consists in running the…
A common goal in observational research is to estimate marginal causal effects in the presence of confounding variables. One solution to this problem is to use the covariate distribution to weight the outcomes such that the data appear…
Detecting dependence between variables is a crucial issue in statistical science. In this paper, we propose a novel metric called label projection correlation to measure the dependence between numerical and categorical variables. The…
We introduce a novel measure of dependence that captures the extent to which a random variable $Y$ is determined by a random vector $X$. The measure equals zero precisely when $Y$ and $X$ are independent, and it attains one exactly when $Y$…
The paper contains results in three areas: First we present a general estimate for tail probabilities of Gaussian quadratic forms with known expectation and variance. Thereafter we analyze the distribution of norms of complex Gaussian…
We present a test for independence of two strictly stationary time series based on a bootstrap procedure for the distance covariance. Our test detects any kind of dependence between the two time series within an arbitrary maximum lag $L$.…
Distance covariance is a popular dependence measure for two random vectors $X$ and $Y$ of possibly different dimensions and types. Recent years have witnessed concentrated efforts in the literature to understand the distributional…
Nonparametric correlations such as Spearman's rank correlation and Kendall's tau correlation are widely applied in scientific and engineering fields. This paper investigates the problem of computing nonparametric correlations on the fly for…
The covariance matrix of a $p$-dimensional random variable is a fundamental quantity in data analysis. Given $n$ i.i.d. observations, it is typically estimated by the sample covariance matrix, at a computational cost of $O(np^{2})$…