A Multivariate Version of Hoeffding’s In- Equality
نویسنده
چکیده
In this paper a multivariate version of Hoeffding’s inequality is proved about the tail distribution of homogeneous polynomials of Rademacher functions with an optimal constant in the exponent of the upper bound. The proof is based on an estimate about the moments of homogeneous polynomials of Rademacher functions which can be considered as an improvement of Borell’s inequality in a most important special case.
منابع مشابه
CS 269 : Machine Learning Theory Lecture 4 : Infinite Function Classes
Before stating Hoeffding’s Inequality, we recall two intermediate results that we will use in order to prove it. One is Markov’s Inequality and other is Hoeffding’s Lemma. (Note that in class we did not cover Hoeffding’s Lemma, and only gave a brief outline of the Chernoff Bounding Techniques and how they are used to prove Hoeffding’s Inequality. Here we give a full proof of Hoeffding’s Inequal...
متن کاملMann - Withney multivariate nonparametric control chart.
In many quality control applications, the necessary distributional assumptions to correctly apply the traditional parametric control charts are either not met or there is simply not enough information or evidence to verify the assumptions. It is well known that performance of many parametric control charts can be seriously degraded in situations like this. Thus, control charts that do not requi...
متن کاملA Multivariate Generalization of Hoeffding’s Inequality
In the study of U -statistics we need a multivariate version of this result. The goal of this paper is to present such an inequality. To formulate it first we have to introduce some notations. Let us fix a positive integer k and some real numbers a(j1, . . . , jk) for all sets of arguments {j1, . . . , jk} such that 1 ≤ jl ≤ n, 1 ≤ l ≤ k, and jl 6= jl′ if l 6= l, in such a way that the numbers ...
متن کاملعدالت جنسیتی با بیعدالتی در نظام آموزشی استان ایلام
Introduction: Educational equality is newly considered in social, political and economic system of the nations. Many conventions, treaties & statements in the world emphasizing these rights have been determined and issued. This issue has been considered in politic, economic and social development plans of Iran. Explaining this issue in undeveloped areas such as Ilam province can provide i...
متن کاملTesting for the Equality of Integration Orders of Multiple Series
Testing for the equality of integration orders is an important topic in time series analysis because it constitutes an essential step in testing for (fractional) cointegration in the bivariate case. For the multivariate case, there are several versions of cointegration, and the version given in Robinson and Yajima (2002) has received much attention. In this definition, a time series vector is p...
متن کامل