The integral of a symmetric unimodal function over a symmetric convex set and some probability inequalities
T. W. Anderson
- Vol. 6, Iss: 2, pp 170-176
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The article was published on 1955-02-01 and is currently open access. It has received 552 citations till now. The article focuses on the topics: Convex set & Subderivative.read more
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A generalized unimodality
TL;DR: A definition -- more exactly, a one parameter family of definitions -- of unimodality for random objects taking values in a finite dimensional vector space and an extension of Khintchine's theorem to alpha-unimodality are given.
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Reflection Groups, Generalized Schur Functions, and the Geometry of Majorization
TL;DR: In this article, a geometrical study of convex polytopes and the ordering of the majorization and Schur-concave functions in reflection groups is presented.
Journal ArticleDOI
Sample path properties of bifractional Brownian motion
Ciprian A. Tudor,Yimin Xiao +1 more
TL;DR: In this paper, the authors prove that B H;K is strongly locally non-deterministic and apply this property to Chung's law of the iterated logarithm.
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Minimax risk of matrix denoising by singular value thresholding
David L. Donoho,Matan Gavish +1 more
TL;DR: In this article, the problem of matrix denoising is solved by applying soft thresholding to the singular values of the noisy measurement, where the noise matrix has i.i.d. Gaussian entries.
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Mutual Information Games in Multiuser Channels With Correlated Jamming
S. Shafiee,Sennur Ulukus +1 more
TL;DR: This work investigates the behavior of two users and one jammer in an additive white Gaussian noise channel with and without fading when they participate in a noncooperative zero-sum game, with the channel's input/output mutual information as the objective function.
References
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Asymptotic Theory of Certain "Goodness of Fit" Criteria Based on Stochastic Processes
TL;DR: In this article, a general method for calculating the limiting distributions of these criteria is developed by reducing them to corresponding problems in stochastic processes, which in turn lead to more or less classical eigenvalue and boundary value problems for special classes of differential equations.
BookDOI
Theorie der Konvexen Körper
T. Bonnesen,W. Fenchel +1 more
TL;DR: In this article, Minkowski et al. den engen Zusammenhang dieser Begriffbildungen und Satze mit der Frage nach der bestimmung konvexer Flachen durch ihre GAusssche Krtim mung aufgedeckt und tiefliegende diesbeztigliche Satze bewiesen.
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The Cramer-Smirnov Test in the Parametric Case
TL;DR: In this paper, the authors extended the Cramer-Smirnov and von Mises test to the parametric case, a suggestion of Cramer [1], see also [2].