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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Reflection groups and a convolution theorem
TL;DR: In this paper, it was shown that if G is a finite linear group that satisfies the Convolution Theorem, then it is a reflection group, and if ρ : G ↪→ GL(V ) is a faithful representation of the Coxeter representation, then ρ is a direct sum of the canonical Coxeter representations of G and a trivial representation.
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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 paper, 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).
The Generalized Elastic Net for least squares regression with network-aligned signal and correlated design
TL;DR: In this article , a generalized elastic net is proposed for regression problems where the feature vectors are indexed by vertices of a given graph and the true signal is believed to be smooth or piecewise constant with respect to this graph.
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On frequentist coverage errors of Bayesian credible sets in moderately high dimensions
Keisuke Yano,Kengo Kato +1 more
TL;DR: It is shown that Bayesian credible bands for those nonparametric models have coverage errors decaying polynomially fast in the sample size, implying advantages of Bayesianredible bands over confidence bands based on extreme value theory.
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Lower functions and Chung's LILs of the generalized fractional Brownian motion
TL;DR: The problem of establishing the Chung-type law of the iterated logarithm of a generalized fractional Brownian motion at t = 0 and at infinity was left open in Wang and Xiao as discussed by the authors .
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.
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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].