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In this communication, we describe some interrelations between generalized $q$-entropies and a generalized version of Fisher information. In information theory, the de Bruijn identity links the Fisher...
In this paper a simple proof of the Chebyshev's inequality for random vectors obtained by Chen (arXiv:0707.0805v2, 2011) is obtained. This inequality gives a lower bound for the percentage of the popu...
We present a graphical approach to deriving inequality constraints for directed acyclic graph (DAG) models, where some variables are unobserved. In particular we show that the observed distribution of...
We give a simple proof of Bell’s inequality in quantum mechanics which, in conjunction with experiments, demonstrates that the local hidden variables assumption is false. The proof sheds light on rela...
We show somewhat unexpectedly that whenever a general Bernstein-type maximal inequality holds for partial sums of a sequence of random variables, a maximal form of the inequality is also valid.
We establish a simple variance inequality for U-statistics whose underlying sequence of random variables is an ergodic Markov Chain.
We investigate a one-parameter family of probability densities (related to the Pareto distribution, which describes many natural phenomena) where the Cram´er-Rao inequality provides no informa...
This paper presents a study of the large-sample behavior of the posterior distribution of a structural parameter which is partially identified by moment inequalities. The posterior density is derive...
Chernoff proves an inequality using Hemite polynomials. Here we prove and generalize this inequality using Cauchy - Schwartz inequality and Fubini equality.
This note contains the proof of a decoupling ineqnality for multilinear functions of symmetric B-valued stable random vectors.
Jensen's inequality for Schwarz maps in von Neumann algebras。
Extensions of Chebychev's inequality with applications。
Using a probabilistic technique we obtain upper and lower estimates for the Poisson kernels of the second order diflerential operators on a homogeneous manifold of negative curvature. Our results i...
We establish a logarithmic Sobolev inequality for a one- -dimensional multivalued stochastic differential equation associated with the subdillerential of a convex lower semicontinuous function, usin...
We prove an exponential inequality for negatively associated and strictly stationary random variables. A condition is given for almost sure convergence and the associated rate of convergence is specif...

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