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

We extend the celebrated Glivenko-Cantelli theorem, sometimes called the fundamental theorem of statistics, from its standard setting of total variation distance to all $f$-divergences. A key obstacle in this endeavor is to define…

Errors in variables (Deming) regression of measurements spanning a wide range of values requires appropriate weighting to reflect nonconstant variance. Precision profile models, mathematical relationships between measurement variance and…

We compare and contrast fourteen measures that have been proposed for the purpose of quantifying partisan gerrymandering. We consider measures that, rather than examining the shapes of districts, utilize only the partisan vote distribution…

Microscopic models describing a whole of economic interactions in a closed society are considered. The presence of a tax system combined with a redistribution process is taken into account, as well as the occurrence of tax evasion. In…

We study a generalized version of Wyner's common information problem (also coined the distributed source simulation problem). The original common information problem consists in understanding the minimum rate of the common input to…

In this short note, we will show that the metric of Deligne's pairing is continous.

This work considers the problem of estimating the distance between two covariance matrices directly from the data. Particularly, we are interested in the family of distances that can be expressed as sums of traces of functions that are…

A method is discussed that allows combining sets of differential or inclusive measurements. It is assumed that at least one measurement was obtained with simultaneously fitting a set of nuisance parameters, representing sources of…

Motivated by putting empirical work based on (synthetic) election data on a more solid mathematical basis, we analyze six distances among elections, including, e.g., the challenging-to-compute but very precise swap distance and the distance…

In this paper, the concept of the classical $f$-divergence for a pair of measures is extended to the mixed $f$-divergence for multiple pairs of measures. The mixed $f$-divergence provides a way to measure the difference between multiple…

This paper presents a distance function between sets based on an average of distances between their elements. The distance function is a metric if the sets are non-empty finite subsets of a metric space. It can be applied to produce various…

The Jensen's inequality plays a crucial role in the analysis of time-delay and sampled-data systems. Its conservatism is studied through the use of the Gr\"{u}ss Inequality. It has been reported in the literature that fragmentation (or…

A robust mean value is often a good alternative to the standard mean value when dealing with data containing many outliers. An efficient method for samples of one-dimensional features and the truncated quadratic error norm is presented and…

The aim of this paper is to establish some new inequalities similar to the Ostrowski's inequalities which are more generalized than the inequalities of Dragomir and Cerone. The current article obtains bounds for the deviation of a function…

We study a family of distance functions on rankings that allow for asymmetric treatments of alternatives and consider the distinct relevance of the top and bottom positions for ordered lists. We provide a full axiomatic characterization of…

A general divergence measure for monotonic functions is introduced. Its connections with the f-divergence for convex functions are explored. The main properties are pointed out.

We propose a generalization of separability in the context of global optimization. Our results apply to objective functions implemented as differentiable computer programs. They are presented in the context of a simple branch and bound…

Parameter estimation via M- and Z-estimation is equally powerful in semiparametric models for one-dimensional functionals due to a one-to-one relation between corresponding loss and identification functions via integration and…

Generative Adversarial Networks (GANs) have been used to model the underlying probability distribution of sample based datasets. GANs are notoriuos for training difficulties and their dependence on arbitrary hyperparameters. One recent…

This paper is devoted to the estimators of the mean that provide strong non-asymptotic guarantees under minimal assumptions on the underlying distribution. The main ideas behind proposed techniques are based on bridging the notions of…