Related papers: Improved distance correlation estimation
Spatial association measures for univariate static spatial data are widely used. When the data is in the form of a collection of spatial vectors with the same temporal domain of interest, we construct a measure of similarity between the…
Asymptotic properties of a dimension-robust dependence measure are investigated. It is related to those used in independence tests, but is derivable, thus suitable for independent component analysis. An adjustable kernel allows to…
The choice of a point set, to be used in numerical integration, determines, to a large extent, the error estimate of the integral. Point sets can be characterized by their discrepancy, which is a measure of its non-uniformity. Point sets…
For distributed estimations in a sensor network, the consistency and accuracy of an estimator are greatly affected by the unknown correlations between individual estimates. An inconsistent or too conservative estimate may degrade the…
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…
Chatterjee's correlation coefficient has recently been proposed as a new association measure for bivariate random vectors that satisfies a number of desirable properties. Among these properties is the feature that the coefficient equals one…
We study an independence test based on distance correlation for random fields $(X,Y)$. We consider the situations when $(X,Y)$ is observed on a lattice with equidistant grid sizes and when $(X,Y)$ is observed at random locations. We provide…
A fundamental method of reconstructing networks, e.g. in the context of gene regulation, relies on the precision matrix (the inverse of the variance-covariance matrix) as an indicator which variables are associated with each other. The…
We investigate two classes of transformations of cosine similarity and Pearson and Spearman correlations into metric distances, utilising the simple tool of metric-preserving functions. The first class puts anti-correlated objects maximally…
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…
It has been recently shown in Jaworski, P., Jelito, D. and Pitera, M. (2024), 'A note on the equivalence between the conditional uncorrelation and the independence of random variables', Electronic Journal of Statistics 18(1), that one can…
This paper considers the problem of estimating the variance of a sum of a triangular array of random vectors with heterogeneous means. When random vectors exhibit two-way cluster dependence or weak dependence, standard variance estimators…
Mutual information is a well-known tool to measure the mutual dependence between variables. In this paper, a Bayesian nonparametric estimation of mutual information is established by means of the Dirichlet process and the $k$-nearest…
This paper develops an intuitive concept of perfect dependence between two variables of which at least one has a nominal scale. Perfect dependence is attainable for all marginal distributions. It furthermore proposes a set of dependence…
Identifying statistical dependence between the features and the label is a fundamental problem in supervised learning. This paper presents a framework for estimating dependence between numerical features and a categorical label using…
Performance estimation under covariate shift is a crucial component of safe AI model deployment, especially for sensitive use-cases. Recently, several solutions were proposed to tackle this problem, most leveraging model predictions or…
Let $\pi\in \Pi(\mu,\nu)$ be a coupling between two probability measures $\mu$ and $\nu$ on a Polish space. In this article we propose and study a class of nonparametric measures of association between $\mu$ and $\nu$, which we call…
In this paper we propose and study a class of nonparametric, yet interpretable measures of association between two random vectors $X$ and $Y$ taking values in $\mathbb{R}^{d_1}$ and $\mathbb{R}^{d_2}$ respectively ($d_1, d_2\ge 1$). These…
Given two sets $x_1^{(1)},\ldots,x_{n_1}^{(1)}$ and $x_1^{(2)},\ldots,x_{n_2}^{(2)}\in\mathbb{R}^p$ (or $\mathbb{C}^p$) of random vectors with zero mean and positive definite covariance matrices $C_1$ and $C_2\in\mathbb{R}^{p\times p}$ (or…
The coefficient of variation is a useful indicator for comparing the spread of values between dataset with different units or widely different means. In this paper we address the problem of investigating the equality of the coefficients of…