Related papers: Modeling coskewness with zero correlation and corr…
We introduce the coverage correlation coefficient, a novel nonparametric measure of statistical association designed to quantifies the extent to which two random variables have a joint distribution concentrated on a singular subset with…
It is well known that while the independence of random variables implies zero correlation, the opposite is not true. Namely, uncorrelated random variables are not necessarily independent. In this note we show that the implication could be…
Collapsibility deals with the conditions under which a conditional (on a covariate W) measure of association between two random variables X and Y equals the marginal measure of association, under the assumption of homogeneity over the…
We investigate the rank of random (symmetric) sparse matrices. Our main finding is that with high probability, any dependency that occurs in such a matrix is formed by a set of few rows that contains an overwhelming number of zeros. This…
We study the impact of dependence uncertainty on the expectation of the product of $d$ random variables, $\mathbb{E}(X_1X_2\cdots X_d)$ when $X_i \sim F_i$ for all~$i$. Under some conditions on the $F_i$, explicit sharp bounds are obtained…
A class of examples concerning the relationship of linear regression and maximal correlation is provided. More precisely, these examples show that if two random variables have (strictly) linear regression on each other, then their maximal…
Not all experiments publish their results with a description of the correlations between the data points. This makes it difficult to do hypothesis tests or model fits with that data, since just assuming no correlation can lead to an over-…
Is it possible to define a coefficient of correlation which is (a) as simple as the classical coefficients like Pearson's correlation or Spearman's correlation, and yet (b) consistently estimates some simple and interpretable measure of the…
We obtain exact analytical expressions for correlations between real zeros of the Kac random polynomial. We show that the zeros in the interval $(-1,1)$ are asymptotically independent of the zeros outside of this interval, and that the…
We study a recently introduced class of scale-free networks showing a high clustering coefficient and non-trivial connectivity correlations. We find that the connectivity probability distribution strongly depends on the fine details of the…
Uncoupled regression is the problem to learn a model from unlabeled data and the set of target values while the correspondence between them is unknown. Such a situation arises in predicting anonymized targets that involve sensitive…
Uncorrelated random scale-free networks are useful null models to check the accuracy an the analytical solutions of dynamical processes defined on complex networks. We propose and analyze a model capable to generate random uncorrelated…
When scholars study joint distributions of multiple variables, copulas are useful. However, if the variables are not linearly correlated with each other yet are still not independent, most of conventional copulas are not up to the task.…
We develop a statistical theory to characterize correlations in weighted networks. We define the appropriate metrics quantifying correlations and show that strictly uncorrelated weighted networks do not exist due to the presence of…
In recent years, the theory and application of complex networks have been quickly developing in a markable way due to the increasing amount of data from real systems and to the fruitful application of powerful methods used in statistical…
Measuring the correlation (association) between two random variables is one of the important goals in statistical applications. In the literature, the covariance between two random variables is a widely used criterion in measuring the…
We consider marginal log-linear models for parameterizing distributions on multidimensional contingency tables. These models generalize ordinary log-linear and multivariate logistic models, besides several others. First, we obtain some…
Improving the detection of relevant variables using a new bivariate measure could importantly impact variable selection and large network inference methods. In this paper, we propose a new statistical coefficient that we call the rank…
The existence of the scaling limit and its universality, for correlations between zeros of {\it Gaussian} random polynomials, or more generally, {\it Gaussian} random sections of powers of a line bundle over a compact manifold has been…
This paper is to prove the asymptotic normality of a statistic for detecting the existence of heteroscedasticity for linear regression models without assuming randomness of covariates when the sample size $n$ tends to infinity and the…