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Hoeffding’s Inequality and Multivariate Majorization
1984Many years ago Hoeffding (1956, Theorem 3) proved the following result: if X1,…, Xn are independent Bernoulli random variables and if $$\psi :\{ 0,...,n\} \to R$$ is (strictly) concave, then $${{\Bbb E}_{\bar p}}\left[ {\psi \left( {\sum\limits_{i = 1}^n {{X_i}} } \right)} \right]\underline { \leqslant \,} {{\Bbb E}_{{p_1},...,{p_n}}}\left[ {
Christian Berg +2 more
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Digital Inequality Across Major Life Realms
American Behavioral Scientist, 2018This issue of the American Behavioral Scientist probes digital inequality as both an endogenous and exogenous factor shaping key life realms and social processes. These include aging and the life course, family and parenting, students and education, prisoner rehabilitation, and social class.
Laura Robinson +3 more
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Inequalities via Majorization — An Introduction
1983This paper provides a brief introduction to the theory of majorization and its use in deriving inequalities. Majorization is a preordering of vectors, and inequalities are obtained from the fact that ϕ(x) ≤ ϕ(y) whenever x is majorized by y and ϕ is an order-preserving function.
Albert W. Marshall, Ingram Olkin
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A note on Slepian’s inequality based on majorization
Statistics & Probability Letters, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ding, Ying, Zhang, Xinsheng
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Some Majorization Inequalities in Multivariate Statistical Analysis
SIAM Review, 1988This paper contains a review of certain majorization inequalities in multivariate statistical analysis. The results apply to a large class of distributions (including the multivariate normal distribution) and have implications in estimation, hypothesis testing, and other related problems in statistics.
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Markoff Type Inequalities for Curved Majorants
1987Let Лn be the set of all polynomials of degree at most n with complex coefficients. As usual denote by $${T_m}(x)\,:\, = \cos \,(m\,arc\,cos\,x)$$ and $${U_m}(x)\;:\; = \;{(1 = {x^2})^{ - 1/2}}\sin ((m + 1)arc\;cos\;x)$$ the Tschebyscheff polynomials of degree m of the first and second kind, respectively. Furthermore, let us write ∥·∥ for
Qazi Ibadur Rahman, Gerhard Schmeisser
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Inequality and Majorization : Robin Hood in Unexpected Places
Calcutta Statistical Association Bulletin, 2011The Lorenz order and its mathematical cousin majorization, best understood as natural consequences of accepting as axiomatic the belief that Robin Hood's activities in robbing the rich to give to the poor reduce inequality in the distribution of wealth, have proved to be useful tools in identifying and extending inequalities in a broad spectrum of ...
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