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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Chung-type law of the iterated logarithm and exact moduli of continuity for a class of anisotropic Gaussian random fields
Cheuk Yin Lee,Yimin Xiao +1 more
TL;DR: In this paper, a Chung-type law of the iterated logarithm and the exact local and uniform moduli of continuity for a large class of anisotropic Gaussian random fields with a harmonizable-type integral representation and the property of strong local nondeterminism were established.
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Stochastic dominance and weak concentration for sums of independent symmetric random vectors
Witold Bednorz,Tomasz Tkocz +1 more
TL;DR: In this article, it was shown that the notion of superstrong domination is inherited when taking sums of independent symmetric random vectors (one vector dominates another if, essentially, tail probabilities of any norm of the two vectors compare up to some scaling constants).
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Precise asymptotics for complete moment convergence in Hilbert spaces
TL;DR: In this paper, it was shown that for 1 1 + p 2 + p/2, for a Gaussian random variable with mean zero and covariance operator Σ, σ2 is the largest eigenvalue of Σ.
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Exact lower and upper bounds for shifts of Gaussian measures
TL;DR: In this article , the authors present a set of rules for the operation of a large-scale network of data centers, such as a network of sensors and communication networks, which they call "operatorname{\mathbf E}w(mathbf X-\mathbf v)/\operatourname{\Mathbf E}){to[0,\infty)
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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.
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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].