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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Optimal controllers for nonsymmetric and nonquadratic loss functions
TL;DR: In this paper, the minimum-variance controller is shown to be optimal for nonsymmetric and non-quadratic loss functions, and for process disturbances driven by normal white noise.
Journal ArticleDOI
Quadratic functionals and small ball probabilities for the $m$-fold integrated Brownian motion
TL;DR: In this article, the Laplace transform of the quadratic functional of the Gaussian process Xm(t) was found by using an appropriate self-adjoint integral operator.
Journal ArticleDOI
Necessary subspace concentration conditions for the even dual Minkowski problem
Martin Henk,Hannes Pollehn +1 more
TL;DR: In this article, tight subspace concentration inequalities for the dual curvature measures of an n-dimensional origin-symmetric convex body for q ≥ n + 1 were shown.
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L2RM: Low-rank Linear Regression Models for High-dimensional Matrix Responses.
TL;DR: A fast and efficient screening procedure based on the spectral norm of each coefficient matrix to deal with the case when the number of covariates is extremely large and a theoretical guarantee for the overall solution of the two-step screening and estimation procedure is established.
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].