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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Minimax estimation with thresholding and its application to wavelet analysis
TL;DR: In this article, the authors proposed a minimax estimator for the wavelet analysis, which performs the best among the well-known estimators aiming simultaneously at estimation and model selection.
Journal ArticleDOI
Covariance bounds for multivariate unimodal distributions and a characterization of uniformity
TL;DR: In this paper, it was shown that a univariate probability distribution with support in [−1, 1] and unimodal with respect to 0 has a variance of at most 13, which is attained only for the uniform distribution.
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Strong Optimality of the Shoot-Adjust-Shoot Strategy
TL;DR: It is shown that seemingly different “adjustment” procedures are equivalent, if viewed in appropriate coordinate systems, and properties of the optimal sequential adjustment procedure are reviewed, including some related to stochastic approximation.
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Monotonicity of certain multivariate normal probabilities
TL;DR: In this article, it was shown that P(X e C, Y e K) is a monotonically increasing function of the first canonical correlation coefficient between X and Y, provided the remaining coefficients are zero.
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Estimation of a Symmetric Distribution
TL;DR: In this article, the authors considered the problem of estimating the shape parameter of a population which is symmetric about zero, and showed that it is asymptotically minimax-efficient in the Hellinger neighborhood.
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].