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The Gaussian model equips strong properties that facilitate studying and interpreting graphical models. Specifically it reduces conditional independence and the study of positive association to determining partial correlations and their…
Linear regression is a data analysis technique, which is categorized as supervised learning. By utilizing known data, we can predict unknown data. Recently, researchers have explored the use of quantum annealing (QA) to perform linear…
Correlation mixtures of elliptical copulas arise when the correlation parameter is driven itself by a latent random process. For such copulas, both penultimate and asymptotic tail dependence are much larger than for ordinary elliptical…
Over the last couple of decades, several copula based methods have been proposed in the literature to test for the independence among several random variables. But these existing tests are not invariant under monotone transformations of the…
A record is an entry in a time series that is larger or smaller than all previous entries. If the time series consists of independent, identically distributed random variables with a superimposed linear trend, record events are positively…
We propose a parsimonious quantile regression framework to learn the dynamic tail behaviors of financial asset returns. Our model captures well both the time-varying characteristic and the asymmetrical heavy-tail property of financial time…
A useful property of independent samples is that their correlation remains the same after applying marginal transforms. This invariance property plays a fundamental role in statistical inference, but does not hold in general for dependent…
The relationship between a response variable and its covariates can vary significantly, especially in scenarios where covariates take on extremely high or low values. This paper introduces a max-linear tail regression model specifically…
Standard Gini covariance and Gini correlation play important roles in measuring the dependence of random variables with heavy tails. However, the asymmetry brings a substantial difficulty in interpretation. In this paper, we propose a…
We introduce Bell inequalities based on covariance, one of the most common measures of correlation. Explicit examples are discussed, and violations in quantum theory are demonstrated. A crucial feature of these covariance Bell inequalities…
Consider a random sample in the max-domain of attraction of a multivariate extreme value distribution such that the dependence structure of the attractor belongs to a parametric model. A new estimator for the unknown parameter is defined as…
Covariate-adaptive randomization (CAR) procedures are frequently used in comparative studies to increase the covariate balance across treatment groups. However, because randomization inevitably uses the covariate information when forming…
Accurately estimating the proportion of true signals among a large number of variables is crucial for enhancing the precision and reliability of scientific research. Traditional signal proportion estimators often assume independence among…
One of the most popular class of tests for independence between two random variables is the general class of rank statistics which are invariant under permutations. This class contains Spearman's coefficient of rank correlation statistic,…
Correlations play a pivotal role in various fields of science, particularly in quantum mechanics, yet their proper quantification remains a subject of debate. In this work, we aim to discuss the challenge of defining a reliable measure of…
The use of Pearson's correlation coefficient in Author Cocitation Analysis was compared with Salton's cosine measure in a number of recent contributions. Unlike the Pearson correlation, the cosine is insensitive to the number of zeros.…
We present sharp tail asymptotics for the density and the distribution function of linear combinations of correlated log-normal random variables, that is, exponentials of components of a correlated Gaussian vector. The asymptotic behavior…
Analysing dependent risks is an important task for insurance companies. A dependency is reflected in the fact that information about one random variable provides information about the likely distribution of values of another random…
The characterization of quantum correlations, being stronger than classical, yet weaker than those appearing in non-signaling models, still poses many riddles. In this work we show that the extent of binary correlations in a general class…
In the present paper, we propose a new rank correlation coefficient $r_n$, which is a sample analogue of the theoretical correlation coefficient $r$, which, in turn, was proposed in the recent work of Stepanov (2025b). We discuss the…