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
Citations
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Two testing problems relating the real and complex multivariate normal distributions
TL;DR: In this paper, the authors consider the problem of testing whether a 2p -dimensional real normal distribution has a p-dimensional complex structure and show that the null and non-null distributions of these distributions are obtained.
Journal ArticleDOI
Limiting Behavior of the Extremum of Certain Sample Functions
TL;DR: In this paper, it was shown that the asymptotic probability of the classical Kolmogorov-Smirnov statistic exceeding any positive real number provides an upper bound for the corresponding probability when the underlying random variables are not necessarily identically distributed.
Journal ArticleDOI
Asymptotic Minimax Character of the Sample Distribution Function for Vector Chance Variables
J. Kiefer,J. Wolfowitz +1 more
TL;DR: In this article, it was shown that the sample distribution function is asymptotically minimax for a large class of weight functions of the type described below, where the loss function is a function of the maximum difference between estimated and true d.f.
Journal ArticleDOI
IG-symmetry and R-symmetry: Interrelations and applications to the inverse Gaussian theory
Govind S. Mudholkar,Hongyue Wang +1 more
TL;DR: In this paper, the root-reciprocal inverse Gaussian (RRIG) distribution is considered and a physically transparent notion of reciprocal symmetry (R-symmetry) is introduced.
Proceedings ArticleDOI
Multistage adaptive estimation of sparse signals
Dennis Wei,Alfred O. Hero +1 more
TL;DR: This paper considers sequential adaptive estimation of sparse signals under a constraint on the total sensing effort, and shows gains up to several dB as compared to recently proposed adaptive methods, and dramatic gains compared to non-adaptive estimation.
References
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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].