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
Citations
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The Poincare map of randomly perturbed periodic motion
TL;DR: The Poincaré map of the randomly perturbed periodic motion is defined, constructed, and analyzed and it is shown that the geometric distribution of the first exit times translates into statistical properties of solutions of important differential equation models in applications.
Concentration inequalities for Gauss-Markov estimators
TL;DR: In this paper, concentration inequalities are given for the Gauss-Markov estimator of the mean vector under various distributional and invariance assumptions on the error vector, which is used to establish monotonicity results relative to a natural group induced partial ordering.
인지의미론에서 본 영어 상호-사건 관계 'and' 접속구문
TL;DR: It is shown that Culicover and Jackendoff's arguments for the coordinate status of their 'and' sentences are not valid and it is discussed that explicature which contains the cross-event relation meaning should be the basis for the analysis of the syntax and semantics interface since it plays a role in syntactic operations like extraction.
Cross-validation and median criterion
Zhong guo Zheng,Ying Yang +1 more
TL;DR: A new method of selecting the smoothing parameter in nonparametric regression called median cross validation (MCV) is suggested, applied to choose the number of nearest neighbors used in estimating the regression function by local sample medians.
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Small deviations of general L\'{e}vy processes
Frank Aurzada,Steffen Dereich +1 more
TL;DR: In this paper, the authors studied the small deviation problem for general real-valued L\'{e}vy processes and showed that a nonvanishing Gaussian component has the same (strong) asymptotic small deviation rate as the corresponding Brownian motion.
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].