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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Dissertation
Studies integrating geometry, probability, and optimization under convexity
TL;DR: This dissertation explores convexity in the intersection of three fields, namely, geometry, probability, and optimization, and studies in depth a variety of geometric quantities used to describe the behavior of different algorithms.
Book ChapterDOI
Stochastic Dominance for Elliptical Distributions: Applications in Bayesian Inference
TL;DR: In this paper, the optimality of the generalized Bayesian estimator with respect to the stochastic dominance relations induced by the posterior distribution of the loss function, whenever the posterior is an elliptical distribution, is proven for general loss functions.
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Monotonicity of the Power Function and Unbiasedness of Some Likelihood Ratio Tests
TL;DR: In this paper, a generalization of the p-dimensional normal distribution is provided by elliptically contoured distributions, and the question of how far these properties are conserved when this more general family of distributions is considered is investigated.
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Exact Uniform Modulus of Continuity for Q-Isotropic Gaussian Random Fields
TL;DR: In this paper , the existence of an exact uniform modulus continuity for the class of q-isotropic Gaussian random processes was proved for a d-dimensional version of the B γ Gaussian processes.
Book ChapterDOI
Integral Inequalities Over A Symmetric Convex Set
TL;DR: In this paper, two fundamental inequalities with greater generality were studied, i.e., the probability content of a convex set that is symmetric about the origin, and a generalization of an inequality of Sidak (see Theorem 2.2.2).
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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].