Related papers: Generalized Non-Symmetric Divergence Measures and …
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…
We present a general non-parametric statistical inference theory for integrals of quantiles without assuming any specific sampling design or dependence structure. Technical considerations are accompanied by examples and discussions,…
We propose a modified $\chi^{\beta}$-divergence, give some of its properties, and show that this leads to the definition of a generalized Fisher information. We give generalized Cram\'er-Rao inequalities, involving this Fisher information,…
In this paper we present a series of results that permit to extend in a direct manner uniform deviation inequalities of the empirical process from the independent to the dependent case characterizing the additional error in terms of…
Parametric adversarial divergences, which are a generalization of the losses used to train generative adversarial networks (GANs), have often been described as being approximations of their nonparametric counterparts, such as the…
Lie symmetry analysis is one of the powerful tools to analyze nonlinear ordinary differential equations. We review the effectiveness of this method in terms of various symmetries. We present the method of deriving Lie point symmetries,…
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 explore the conditions for the existence of Noether symmetries in the dynamics of FRW metric, non minimally coupled with a scalar field, in the most general situation, and with nonzero spatial curvature. When such symmetries are present…
The present paper is devoted to the study of Jensen-Mercer-type inequalities. Our results generalize and improve some earlier results in the literature.
The geometric Jensen--Shannon divergence (G-JSD) gained popularity in machine learning and information sciences thanks to its closed-form expression between Gaussian distributions. In this work, we introduce an alternative definition of the…
Considering the simultaneous measurement of non-commuting observables, we define a geometric measure for the degree of non-commuting behavior of quantum measurements coming from the initial and final states of the measurements. The…
Asymptotic equivalence results for nonparametric regression experiments have always assumed that the variances of the observations are known. In practice, however the variance of each observation is generally considered to be an unknown…
Nonparametric generalized likelihood ratio test is popularly used for model checking for regressions. However, there are two issues that may be the barriers for its powerfulness. First, the bias term in its liming null distribution causes…
We study a family of inequalities on pairs of measure spaces involving functions defined on product domains. Our main result establishes a Jensen-type inequality under a general product-measure framework, extending classical inequalities…
The asymptotic distribution of the likelihood-ratio statistic for testing parameters on the boundary is well known to be a chi-squared mixture. The mixture weights have been shown to correspond to the intrinsic volumes of an associated…
We suggest generalized robustness for quantifying nonlocality and derive its equivalence to the maximum violation ratio of Bell inequalities defined as vectors with non-negative elements. We investigate its properties by comparing it with…
In this paper, we use the semi-group method and an adaptation of the $L^2-$method of H\"ormander to establish some $\Phi-$entropy inequalities and asymmetric covariance estimates for the strictly convex measures in $\mathbb R^n$. These…
In this work, the probability of an event under some joint distribution is bounded by measuring it with the product of the marginals instead (which is typically easier to analyze) together with a measure of the dependence between the two…
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,…
The issue of asymmetric uncertainties resulting from fits, nonlinear propagation and systematic effects is reviewed. It is shown that, in all cases, whenever a published result is given with asymmetric uncertainties, the value of the…