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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Stochastic ordering of Gini indexes for multivariate elliptical random variables.
TL;DR: In this paper, the authors established the stochastic ordering of the Gini indexes for multivariate elliptical risks and generalized the corresponding results for multiivariate normal risks, showing that several conditions on dispersion matrices and the components of dispersion matrix for the monotonicity of Gini index in the usual stochastically ordered order proposed by Samanthi, Wei and Brazauskas (2016) and Kim and Kim (2019) are also suitable for multicloudical risks.
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Bounds and approximations for distributions of weighted Kolmogorov-Smirnov tests
TL;DR: In this paper, the problem of finding of distributions of one-sided wKS statistics was reduced to the nonlinear boundary crossing problem for a Brownian motion and theoretical estimates of accuracy of the approximations using piecewise linear boundaries were derived.
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A lim inf result for the increments of the Wiener process under theL2-norm
TL;DR: In this article, the authors proved an almost sure lower limit for the square integral of the large increments of the Wiener process, extending results obtained by Li (1992) and Li (1993).
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Inequalities for estimative and predictive probabilities
Abstract: Let μE be the estimative and μP the predictive measures for assessing Gaussian probabilities. It is shown for convex symmetric sets A that μE(A) μP(A) and that similar inequalities hold between members of a sequence of predictive measures. An application yields inequalities for generalized indices of atypicality associated with the two methods.
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An optimal Hardy-Littlewood-Sobolev inequality on $\mathbf R^{n-k} \times \mathbf R^n$ and its consequences
TL;DR: In this article, the Stein-Weiss inequality was shown to be an optimal Hardy-Littlewood-Sobolev inequality for the case of n > k, and the existence of an optimal pair for this inequality was studied.
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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].