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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Non-asymptotic Confidence Estimation of the Autoregressive Parameter in AR(1) Process with an Unknown Noise Variance
TL;DR: In this paper, the estimation problem of the autoregressive parameter in the first-order auto-gressive process with Gaussian noises when the noise variance is unknown is considered, and a nonasymptotic technique is proposed to compensate the unknown variance, and then a point estimator with any prescribed mean square accuracy is proposed.
A general adaptive framework for multivariate point null testing
TL;DR: In this paper , a general framework for testing a multivariate point null hypothesis is proposed, in which the test statistic is adaptively selected to provide increased power, and theoretical large-sample guarantees for the test under both fixed and local alternatives.
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].