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The categorical Gini correlation proposed by Dang et al. is a dependence measure to characterize independence between categorical and numerical variables. The asymptotic distributions of the sample correlation under dependence and…
Standard Gaussian graphical models (GGMs) implicitly assume that the conditional independence among variables is common to all observations in the sample. However, in practice, observations are usually collected form heterogeneous…
This paper derives closed-form unbiased estimators of central moments in multilevel random-effects models with unbalanced group sizes. In a two-level model, we provide unbiased estimators for the second, third, and fourth central moments…
Classical measures of inequality use the mean as the benchmark of economic dispersion. They are not sensitive to inequality at the left tail of the distribution, where it would matter most. This paper presents a new inequality measurement…
Some probability distributions have moments, and some do not. For example, the normal distribution has power moments of arbitrary order, but the Cauchy distribution does not have power moments. In this paper, by analogy with the…
In this paper we study the asymptotics of linear regression in settings with non-Gaussian covariates where the covariates exhibit a linear dependency structure, departing from the standard assumption of independence. We model the covariates…
In this note we give a combinatorial and non-computational proof of the asymptotics of the integer moments of the moments of the characteristic polynomials of Haar distributed unitary matrices as the size of the matrix goes to infinity.…
We present an approximate expression for the covariance of the log-average periodogram for a zero mean stationary Gaussian process. Our findings extend the work of [1] on the covariance of the log-periodogram by additionally taking…
Uniform bin width histograms are widely used so this data graphic should represent data as correctly as possible. Method of moments based on familiar mean, variance and Fisher-Pearson skewness cure this problem.
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…
Fractional moments have been investigated by many authors to represent the density of univariate and bivariate random variables in different contexts. Fractional moments are indeed important when the density of the random variable has…
The covariance of two random variables measures the average joint deviations from their respective means. We generalise this well-known measure by replacing the means with other statistical functionals such as quantiles, expectiles, or…
This work is an extension of our earlier article, where a well-known integral representation of the logarithmic function was explored, and was accompanied with demonstrations of its usefulness in obtaining compact, easily-calculable, exact…
We establish several optimal moment comparison inequalities (Khinchin-type inequalities) for weighted sums of independent identically distributed symmetric discrete random variables which are uniform on sets of consecutive integers.…
Given a random variable $X$ and considered a family of its possible distortions, we define two new measures of distance between $X$ and each its distortion. For these distance measures, which are extensions of the Gini's mean difference,…
It has been proposed that complex populations, such as those that arise in genomics studies, may exhibit dependencies among observations as well as among variables. This gives rise to the challenging problem of analyzing unreplicated…
Based on measure transportation ideas and the related concepts of center-outward quantile functions, we propose multiple-output center-outward generalizations of the traditional univariate concepts of Lorenz and concentration functions, and…
Exceptional orthogonal Laguerre polynomials can be viewed as an extension of the classical Laguerre polynomials per excluding polynomials of certain order(s) from being eigenfunctions for the corresponding exceptional differential operator.…
Covariance estimation becomes challenging in the regime where the number p of variables outstrips the number n of samples available to construct the estimate. One way to circumvent this problem is to assume that the covariance matrix is…
We propose a probabilistic enhancement of standard kernel Support Vector Machines for binary classification, in order to address the case when, along with given data sets, a description of uncertainty (e.g., error bounds) may be available…