相关论文: Generalized Gini's mean difference through distort…

Given an affine transformation $T$, we define its Fisher distortion $Dist_F(T)$. We show that the Fisher distortion has Riemannian metric structure and provide an algorithm for finding mean distorting transformation -- namely -- for a given…

The degree to which subjects differ from each other with respect to certain properties measured by a set of variables, plays an important role in many statistical methods. For example, classification, clustering, and data visualization…

The geometric median, a notion of center for multivariate distributions, has gained recent attention in robust statistics and machine learning. Although conceptually distinct from the mean (i.e., expectation), we demonstrate that both are…

Vine copulas are a useful statistical tool to describe the dependence structure between several random variables, especially when the number of variables is very large. When modeling data with vine copulas, one often is confronted with a…

In this paper, we propose an estimator of the generalized maximum mean discrepancy between several distributions, constructed by modifying a naive estimator. Asymptotic normality is obtained for this estimator both under equality of these…

Via an axiomatic approach, we characterize the family of n-th order Gini deviation, defined as the expected range over n independent draws from a distribution, to quantify joint dispersion across multiple observations. This family extends…

For a random variable we can define a variational relationship with practical physical meaning as dI=dbar(x)-bar(dx), where I is called as uncertainty measurement. With the help of a generalized definition of expectation,…

In this paper we shall consider some famous means such as arithmetic, harmonic, geometric, root square mean, etc. Considering the difference of these means, we can establish. some inequalities among them. Interestingly, the difference of…

We bound the variance and other moments of a random vector based on the range of its realizations, thus generalizing inequalities of Popoviciu (1935) and Bhatia and Davis (2000) concerning measures on the line to several dimensions. This is…

In this note we present a refinement of the AM-GM inequality, and then we estimate in a special case the typical size of the improvement.

Identifying statistical dependence between the features and the label is a fundamental problem in supervised learning. This paper presents a framework for estimating dependence between numerical features and a categorical label using…

The energy distance and energy scores became important tools in multivariate statistics and multivariate probabilistic forecasting in recent years. They are both based on the expected distance of two independent samples. In this paper we…

In this paper, we draw attention to a promising yet slightly underestimated measure of variability - the Gini coefficient. We describe two new ways of defining and interpreting this parameter. Using our new representations, we compute the…

We obtain the estimate of difference between binomial and generalized binomial distributions in $\chi^2$ metric and in several other related metrics

Comparative convexity is a generalization of convexity relying on abstract notions of means. We define the Jensen divergence and the Jensen diversity from the viewpoint of comparative convexity, and show how to obtain the generalized…

Comparing and recognizing metrics can be extraordinarily difficult because of the group of diffeomorphisms. Two metrics, that could even be the same, could look completely different in different coordinates. This is the gauge problem. The…

We generalize the measurement using an expanded concept of cover, in order to provide a new approach to size of set other than cardinality. The generalized measurement has application backgrounds such as a generalized problem in dimension…

The most general form of a marginal extended perturbation in a two-dimensional system is deduced from scaling considerations. It includes as particular cases extended perturbations decaying either from a surface, a line or a point for which…

We propose statistical procedures for detecting changes in the mean of spatial random fields observed on regular grids. The proposed framework provides a general approach to change detection in spatial processes. Extending a block-based…

In this paper, we propose two new flexible Gini indices (extended lower and upper) defined via differences between the $i$-th observation, the smallest order statistic, and the largest order statistic, for any $1 \leqslant i \leqslant m$.…