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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Randomized Isoperimetric Inequalities
Grigoris Paouris,Peter Pivovarov +1 more
TL;DR: In this article, the authors discuss isoperimetric inequalities for convex sets and show that many such inequalities admit stronger randomized forms in the following sense: for natural families of associated random convex set one has stochastic dominance for various functionals such as volume, surface area, mean width and others.
Journal ArticleDOI
Group Iterative Spectrum Thresholding for Super-Resolution Sparse Spectral Selection
TL;DR: A new regularization approach to handle model collinearity and obtain parsimonious frequency selection simultaneously is proposed, which takes advantage of the pairing structure of sine and cosine atoms in the frequency dictionary.
Journal ArticleDOI
Valid post-selection inference in model-free linear regression
Arun Kumar Kuchibhotla,Lawrence D. Brown,Andreas Buja,Junhui Cai,Edward I. George,Linda Zhao +5 more
TL;DR: In this paper, the authors proposed computationally efficient confidence regions, named UPoSI, for linear OLS regression allowing misspecification of the normal linear model, and for independent as well as some types of dependent data.
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On low-dimensional projections of high-dimensional distributions
TL;DR: In this paper, necessary and sufficient conditions for the Diaconis-Freedman effect were provided in a suitable asymptotic framework with increasing dimension q, and the conditions were proved to be sufficient but necessary as well.
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].