Related papers: Calculating correlation coefficient for Gaussian c…

A generic, model-independent method for the analysis of the two-particle short-range correlations is presented, that can be utilized to describe e.g. Bose-Einstein (HBT or GGLP), statistical, dynamical or other short-range correlation…

Multiple orthogonal polynomials satisfy a number of recurrence relations, in particular there is a $(r+2)$-term recurrence relation connecting the type II multiple orthogonal polynomials near the diagonal (the so-called step-line recurrence…

Data with uncertain, missing, censored, and correlated values are commonplace in many research fields including astronomy. Unfortunately, such data are often treated in an ad hoc way in the astronomical literature potentially resulting in…

Context: Two-point correlation functions are used throughout cosmology as a measure for the statistics of random fields. When used in Bayesian parameter estimation, their likelihood function is usually replaced by a Gaussian approximation.…

The estimation of dependencies between multiple variables is a central problem in the analysis of financial time series. A common approach is to express these dependencies in terms of a copula function. Typically the copula function is…

This paper studies the problem of estimating a covariance matrix from correlated sub-Gaussian samples. We consider using the correlated sample covariance matrix estimator to approximate the true covariance matrix. We establish…

We compute the quantum maximal correlation for bipartite Gaussian states of continuous-variable systems. Quantum maximal correlation is a measure of correlation with the monotonicity and tensorization properties that can be used to study…

Using random matrix technique we determine an exact relation between the eigenvalue spectrum of the covariance matrix and of its estimator. This relation can be used in practice to compute eigenvalue invariants of the covariance…

For extreme value copulas with a known upper tail dependence coefficient we find pointwise upper and lower bounds, which are used to establish upper and lower bounds of the Spearman and Kendall correlation coefficients. We shown that in all…

For a given positive random variable $V>0$ and a given $Z\sim N(0,1)$ independent of $V$, we compute the scalar $t_0$ such that the distance between $Z\sqrt{V}$ and $Z\sqrt{t_0}$ in the $L^2(\R)$ sense, is minimal. We also consider the same…

Learning the joint dependence of discrete variables is a fundamental problem in machine learning, with many applications including prediction, clustering and dimensionality reduction. More recently, the framework of copula modeling has…

Thanks to their ability to capture complex dependence structures, copulas are frequently used to glue random variables into a joint model with arbitrary marginal distributions. More recently, they have been applied to solve statistical…

We consider the simultaneous and continuous measurement of qubit observables $\sigma_z$ and $\sigma_z\cos\varphi + \sigma_x\sin\varphi$, focusing on the temporal correlations of the two output signals. Using quantum Bayesian theory, we…

A convergent approximation is proposed for a mean field density-density correlation function in a system with a two-phase interface. It is based on a fourth-order expansion of the Hamiltonian in terms of fluctuations around the equilibrium…

Not a matter of serious contention, Pearson's correlation coefficient is still the most important statistical association measure. Restricted to just two variables, this measure sometimes doesn't live up to users' needs and expectations.…

We study estimation of an $s$-sparse signal in the $p$-dimensional Gaussian sequence model with equicorrelated observations and derive the minimax rate. A new phenomenon emerges from correlation, namely the rate scales with respect to…

We define a multivariate medial correlation coefficient that extends the probabilistic interpretation and properties of Blomqvist's $\beta$ coefficient, incorporates multivariate marginal dependencies and it preserves a stronger…

We give an explicit formula for the correlation functions of real zeros of a random polynomial with arbitrary independent continuously distributed coefficients.

We examine the dependence of the spatial two-point correlation function of quasars $\xi_{qq}(r,z)$ at different redshifts on the initial power spectrum in flat cosmological models. Quasars and other elements of the large-scale structure of…

Context. Whenever correlation functions are used for inference about cosmological parameters in the context of a Bayesian analysis, the likelihood function of correlation functions needs to be known. Usually, it is approximated as a…