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We investigate testing of the hypothesis of independence between a covariate and the marks in a marked point process. It would be rather straightforward if the (unmarked) point process were independent of the covariate and the marks. In…
The problem of measuring conditional dependence between two random phenomena arises when a third one (a confounder) has a potential influence on the amount of information between them. A typical issue in this challenging problem is 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…
We construct and analyze an estimator of association between random variables based on their similarity in both direction and magnitude. Under special conditions, the proposed measure becomes a robust and consistent estimator of the linear…
Pearson's Chi-squared test, though widely used for detecting association between categorical variables, exhibits low statistical power in large sparse contingency tables. To address this limitation, two novel permutation tests have been…
In this paper we propose several variants to perform the independence test between two random elements based on recurrence rates. We will show how to calculate the test statistic in each one of these cases. From simulations we obtain that…
In this paper we introduce a new measure of conditional dependence between two random vectors ${\boldsymbol X}$ and ${\boldsymbol Y}$ given another random vector $\boldsymbol Z$ using the ball divergence. Our measure characterizes…
Bell inequalities rely on an assumption that the probabilities of adopting configurations of hidden variables describing a system prior to measurement are independent of the choice of measured physical property, also known as measurement…
Measuring and testing dependence between complex objects is of great importance in modern statistics. Most existing work relied on the distance between random variables, which inevitably required the moment conditions to guarantee the…
In data science, it is often required to estimate dependencies between different data sources. These dependencies are typically calculated using Pearson's correlation, distance correlation, and/or mutual information. However, none of these…
We show that the stochastic independence of real-valued random variables is equivalent to the conditional uncorrelation, where the conditioning takes place over the Cartesian products of intervals. Next, we express the mutual independence…
The standard linear and logistic regression models assume that the response variables are independent, but share the same linear relationship to their corresponding vectors of covariates. The assumption that the response variables are…
A method to estimate the time-dependent correlation via an empirical bias estimate of the time-delayed mutual information for a time-series is proposed. In particular, the bias of the time-delayed mutual information is shown to often be…
Quantification of relations between measured variables of interest by statistical measures of dependence is a common step in analysis of climate data. The term "connectivity" is used in the network context including the study of complex…
Motivated by a neuroscience question about synchrony detection in spike train analysis, we deal with the independence testing problem for point processes. We introduce non-parametric test statistics, which are rescaled general…
Measuring conditional dependence is an important topic in statistics with broad applications including graphical models. Under a factor model setting, a new conditional dependence measure based on projection is proposed. The corresponding…
We describe a method to determine the eigenvalue density of empirical covariance matrix in the presence of correlations between samples. This is a straightforward generalization of the method developed earlier by the authors for…
A new index based on empirical copulas, termed the Copula Statistic (CoS), is introduced for assessing the strength of multivariate dependence and for testing statistical independence. New properties of the copulas are proved. They allow us…
Given a random sample of size $n$ from a $p$ dimensional random vector, where both $n$ and $p$ are large, we are interested in testing whether the $p$ components of the random vector are mutually independent. This is the so-called complete…
Measuring dependence between two events, or equivalently between two binary random variables, amounts to expressing the dependence structure inherent in a $2\times 2$ contingency table in a real number between $-1$ and $1$. Countless such…