We provide necessary and sufficient conditions for the validity of the inequality of Simes (1986) in models with elliptical dependencies. Necessary conditions are presented in terms of sufficient conditions for the reverse Simes inequality. One application of our main results concerns the problem of model misspecification, in particular the case that the assumption of Gaussianity of test statis...

We describe hashing of data bases as a problem of information and coding theory. It is shown that the triangle inequality for the Hamming distances between binary vectors may essentially decrease the computational eeorts of a search for a pattern in the data base. Introduction of the Lee distance in the space, which consists of the Hamming distances, leads to a new metric space where the triang...

We consider the sum of squared logarithms inequality and investigate possible connections with the theory of majorization. We also discuss alternative sufficient conditions on two sets of vectors a,b ∈ R+ so that n ∑ i=1 (logai) n ∑ i=1 (logbi) . Generalizations of some inequalities from information theory are obtained, including a generalized information inequality and a generalized log sum in...

A cyclic sum S(x) ■ T.x¡/(xj+i + x, + 2) 's formed with the N components of a vector x, where xN+l « JCj, xN+2 =• x2, and where all denominators are positive and all numerators are nonnegative. It is known that there exist vectors x for which S(x) < N/2 if N > 14 and even, and if N > 25. It has been proved that the inequality S(\) > N/2 holds for N ^ 12. Although it has been conjectured repeate...

This article proves an exponential probability tail inequality for positive semidefinite quadratic forms in a subgaussian random vector. The bound is analogous to one that holds when the vector has independent Gaussian entries.

This paper investigates the effects of inequality in the presence of voluntary risk-sharing. In any period, an agent’s resources are composed of his share of a secure endowment (wealth, land) and a random component (labor income). To be sure, the distribution of wealth does not affect the Pareto optimal payoff vectors but, by changing the autarchic utilities, affects the set of these payoff vec...

in this paper a general view of the gini decomposition is presented. in order to decompose the gini coefficient into within group inequality, between group inequality and transvariation inequality of the iranian urban and rural areas, the 2006 and 2010  micro-data and dagum (1997) method is used. the results indicate that about 48 percent of the inequality in the country as a whole has been due...

A Grüss type inequality for sequences of vectors in inner product spaces which complement a recent result from [6] and applications for differentiable convex functions defined on inner product spaces and applications for Fourier and Mellin transforms, are given.

In this article we provide generalizations of Niezgoda inequality for similarly separable vectors followed by refinements. We also highlight its importance giving applications. Our results will be generalizing many previously established results.

1. Vector Spaces 1 2. Norms 4 2.1. Unit Vectors 6 2.2. Convexity 9 3. Inner Product Spaces 9 3.1. Induced Norms and the CBS Inequality 12 3.2. Orthogonal Sets of Vectors 15 3.3. Best Approximations and Least Squares Problems 17 4. Linear Operators 20 4.1. Operator Norms 22 5. Metric Spaces and Analysis 23 5.1. Metric Spaces 23 5.2. Calculus and Analysis 25 6. Numerical Analysis 26 6.1. Big Oh N...