相关论文: On the efficiency of Gini's mean difference

Let P be a set of points in R^d, and let M be a function that maps any subset of P to a positive real number. We examine the problem of computing the exact mean and variance of M when a subset of points in P is selected according to a…

By combining a bound on the absolute value of the difference of mutual information between two joint probablity distributions with a fixed variational distance, and a bound on the probability of a maximal deviation in variational distance…

We generalize the well-known mean value inequality of subharmonic functions for a slightly more general function class. We also apply this generalized mean value inequality to weighted boundary behavior and nonintegrability questions of…

Starting with a novel definition of divided differences, this essay derives and discusses the basic properties of, and facts about, (univariate) divided differences.

A wide variety of approaches to estimate the degree of synchrony between two or more spike trains have been proposed. One of the most recent methods is the ISI-distance which extracts information from the interspike intervals (ISIs) by…

Let $d_1\leq d_2\leq\ldots\leq d_{n\choose 2}$ denote the distances determined by $n$ points in the plane. It is shown that $\min\sum_i (d_{i+1}-d_i)^2=O(n^{-6/7})$, where the minimum is taken over all point sets with minimal distance $d_1…

A common way to quantify the ,,distance'' between measures is via their discrepancy, also known as maximum mean discrepancy (MMD). Discrepancies are related to Sinkhorn divergences $S_\varepsilon$ with appropriate cost functions as…

Different strategies of reliability theory for the analysis of coherent systems have been studied by various researchers. Here, the Gini-type index is utilized as an applicable tool for the study and comparison of the ageing properties of…

The Gini index does not give a strictly consistent scoring rule in general. Therefore, maximizing the Gini index may lead to wrong decisions. The main issue is that the Gini index is a rank-based score that is not calibration-sensitive. We…

We prove the universality of the large deviations for conjugacy invariant permutations with few cycles. As an application, we establish the universality of large deviation at speeds $n$ and $\sqrt{n}$ for the length of monotone subsequences…

In Bayesian inference, an unknown measurement uncertainty is often quantified in terms of a Gamma distributed precision parameter, which is impractical when prior information on the standard deviation of the measurement uncertainty shall be…

In this paper, we establish the stochastic ordering of the Gini indexes for multivariate elliptical risks which generalized the corresponding results for multivariate normal risks. It is shown that several conditions on dispersion matrices…

The Jensen inequality is a widely used tool in a multitude of fields, such as for example information theory and machine learning. It can be also used to derive other standard inequalities such as the inequality of arithmetic and geometric…

In this paper we obtain some existence result of solution for general variational inequalities. As applications several coincidence and fixed point results are provided.

We propose a new method for estimating causal effects in longitudinal/panel data settings that we call generalized difference-in-differences. Our approach unifies two alternative approaches in these settings: ignorability estimators (e.g.,…

We study the weighted total variation distance between probability measures. Using Fourier-analytic tools, we present estimates in terms of Wasserstein distances between the respective probabilities, under appropriate smoothness and moment…

Wasserstein distances provide a powerful framework for comparing data distributions. They can be used to analyze processes over time or to detect inhomogeneities within data. However, simply calculating the Wasserstein distance or analyzing…

"The rich are getting richer" implies that the population income distributions are getting more right skewed and heavily tailed. For such distributions, the mean is not the best measure of the center, but the classical indices of income…

In this paper, we derive a general representation for the expectation of the Gini coefficient estimator in terms of the Laplace transform of the underlying distribution, together with the mean and the Gini coefficient of its exponentially…

Inequality is an inherent part of our lives: we see it in the distribution of incomes, talents, resources, and citations, amongst many others. Its intensity varies across different environments: from relatively evenly distributed ones, to…