Related papers: A Note on Concentration Inequalities for U-Statist…
We deduce in this paper the sufficient conditions for weak convergence of centered and normed deviation of the u-statistics with values in the space of the real valued continuous function defined on some compact metric space. We obtain also…
The main objective of the paper is to establish explicit estimates on some applicable inequalities in two variables on time scales which can be used in the study of certain qualitative properties of dynamical equations on time scales.
Azuma's inequality is a tool for proving concentration bounds on random variables. The inequality can be thought of as a natural generalization of additive Chernoff bounds. On the other hand, the analogous generalization of multiplicative…
This paper presents the asymptotic theory for nondegenerate $U$-statistics of high frequency observations of continuous It\^{o} semimartingales. We prove uniform convergence in probability and show a functional stable central limit theorem…
In this paper, we consider U-statistics whose data is a strictly stationary sequence which can be expressed as a functional of an i.i.d. one. We establish a strong law of large numbers, a bounded law of the iterated logarithms and a central…
Concentration results and probabilistic analysis for combinatorial problems like the TSP, MWST, graph coloring have received much attention, but generally, for i.i.d. samples (i.i.d. points in the unit square for the TSP, for example).…
Genetic data are frequently categorical and have complex dependence structures that are not always well understood. For this reason, clustering and classification based on genetic data, while highly relevant, are challenging statistical…
Concentration of measure is studied, and obtained, for stable and related random vectors.
For noncorrelated random variables, we study a concentration property of the family of distributions of normalized sums formed by sequences of times of a given large length.
Concentration inequalities are widely used for analyzing machine learning algorithms. However, current concentration inequalities cannot be applied to some of the most popular deep neural networks, notably in natural language processing.…
Empirical evidence demonstrates that citations received by scholarly publications follow a pattern of preferential attachment, resulting in a power-law distribution. Such asymmetry has sparked significant debate regarding the use of…
This is a survey of recent developments in the area of transport inequalities. We investigate their consequences in terms of concentration and deviation inequalities and sketch their links with other functional inequalities and also large…
This article offers different proofs of ten inequalities from those already published. So that the readers can see for themselves, the tasks specified in the condition of the source and classical inequalities which used in previously…
In this paper, we study the asymptotic distribution of some U-statistics whose entries are functions of empirical moments computed from non-overlapping consecutive blocks of an underlying weakly dependent process. The length of these blocks…
In this note, we revisit a classical problem related to the density of nonlinear statistics. We obtain a new representation of densities and, for the first time, a necessary and sufficient condition for the existence of densities is…
A Bernstein-type exponential inequality for (generalized) canonical U-statistics of order 2 is obtained and the Rosenthal and Hoffmann-J{\o}rgensen inequalities for sums of independent random variables are extended to (generalized)…
The main purpose of the present article is to give some new Hilbert's sum type inequalities, which in special cases yield the classical Hilbert's inequalities. Our results provide some new estimates to these types of inequalities.
This book is not meant to be another compendium of select inequalities, nor does it claim to contain the latest or the slickest ways of proving them. This project is rather an attempt at describing how most functional inequalities are not…
In a large, possibly infinite population, each subject is colored red with probability $p$, independently of the others. Then, a finite sub-population is selected, possibly as a function of the coloring. The imbalance in the sub-population…
We prove concentration inequalities for functions of independent random variables {under} sub-gaussian and sub-exponential conditions. The utility of the inequalities is demonstrated by an extension of the now classical method of Rademacher…