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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Journal ArticleDOI
Matrix equivalence classes with applications
Donald R. Jensen,S.S Srinivasan +1 more
TL;DR: In this article, a definite matrix Σ is represented in terms of a semidefinite matrix Ω and a vector γ, such that ( Ω, γ ) may be recovered explicitly from Σ.
Book ChapterDOI
Asymptotic Optimality of Estimators
TL;DR: The nonasymptotic theory, which flourished between 1940 and 1960, ended up as a collection of results that does not amount to a consistent theory as mentioned in this paper, which is the case of non-symmetric theory.
Journal ArticleDOI
Chung’s law of the iterated logarithm for subfractional Brownian motion
TL;DR: In this article, the authors provide a sufficient condition for a self-similar Gaussian process to be strongly locally nondeterministic and show that XH has the property of strong local nondeterminism.
Posted Content
Optimal bounds on the modulus of continuity of the uncentered Hardy-Littlewood maximal function
TL;DR: In this article, the modulus of continuity of the uncentered maximal function in terms of modulus-of-continuity of the given function was derived via integral formulas, and the best constants for Lipschitz and H\"older functions on proper subintervals of R were derived.
Journal ArticleDOI
Directional monotonicity properties of the power functions of likelihood ratio tests for cone-restricted hypotheses of normal means
TL;DR: In this paper, it was shown that the power function of the likelihood ratio test has a certain monotonicity property with respect to the direction of the alternatives in a cone-restricted testing problem.
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].