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
Mathematical foundations of infinite-dimensional statistical models
Evarist Giné,Richard Nickl +1 more
TL;DR: This chapter discusses nonparametric statistical models, function spaces and approximation theory, and the minimax paradigm, which aims to provide a model for adaptive inference oflihood-based procedures.
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A matrix handbook for statisticians
TL;DR: An essential, one-of-a-kind book for graduate-level courses in advanced statistical studies including linear and nonlinear models, multivariate analysis, and statistical computing, and it also serves as an excellent self-study guide for statistical researchers.
Journal ArticleDOI
Convex set functions ind-space
TL;DR: In this article, it was shown that a convex subset of Euclidean d-space R d is convex (concave) if the inequality F(OA + (1 O)B)
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Gaussian processes: Inequalities, small ball probabilities and applications
Wenbo V. Li,Qi-Man Shao +1 more
TL;DR: In this paper, the authors focus on the inequalities, small-ball probabilities, and application of Gaussian processes, and find that the small ball probability is a key step in studying the lower limits of the Gaussian process.
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A Quality Index Based on Data Depth and Multivariate Rank Tests
Regina Y. Liu,Kesar Singh +1 more
TL;DR: The Parameter Q = Q(F, G) as mentioned in this paper measures the Overall "outlyingness" of population G relative to population F and is defined using any concept of data depth, its value ranges from 0 to 1, and is.5 when F and G are identical.
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Journal ArticleDOI
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].