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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MonographDOI
Uniform Central Limit Theorems: Notation Index
TL;DR: In this paper, Donsker's theorem, metric entropy and inequalities, and the universal and uniform central limit theorems are discussed. But they do not consider the two-sample case, the bootstrap case, and confidence sets.
Journal ArticleDOI
Statistical completion of a partially identified graph with applications for the estimation of gene regulatory networks.
TL;DR: The proposed method could facilitate studying underlying lung cancer mechanisms and identifying reliable biomarkers for lung cancer prognosis and show that the partially identified dependent structure reduces the error in estimating the dependent structure.
Posted Content
The Gaussian Correlation Inequality for Symmetric Convex Sets
TL;DR: In this article, the authors proved the Gaussian correlation conjecture that the measure of the intersection of any two symmetric convex sets is greater than or equal to the product of their measures.
Journal ArticleDOI
Reciprocal symmetry, unimodality and Khintchine's theorem
TL;DR: In this paper, the authors explore a number of interesting results and interplays involving reciprocal symmetry, unimodality and Khintchine's theorem with particular emphasis on R-symmetry.
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Bayesian point estimation and prediction
TL;DR: This paper investigates the properties of Bayesian point estimates under other loss functions; both the general case and two special cases (power and exponential loss functions) are considered.
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.
Journal ArticleDOI
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].