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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.

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All of Linear Regression

TL;DR: In this paper, the authors consider the problem of estimating the OLS estimator under variable selection and variable misspecification and variable selection, and derive a deterministic inequality which holds for any set of observations and any sample size.
Journal ArticleDOI

Progressive censoring under inverse sampling for nonparametric two-sample problems

TL;DR: In this article, a progressive censoring test procedure corresponding to the inverse binomial sample is proposed, and different large sample results of the proposed tests are formulated and examined, and the proposed test procedure is evaluated.
Journal ArticleDOI

Sidak-type simultaneous confidence intervals for the risk measures rsmr, based on proportional mortality measures in epidemiologic 1 studies involving several competing risks of death

TL;DR: In this article, simultaneous confidence interval estimates are constructed for the mortality measures RSMR and SPMR based on propor¬tional mortality measures SPMRs in epidemiologic studies for several competing risks of death to which the individuals in the study are exposed.
Book ChapterDOI

Gaussian Measure of a Small Ball and Capacity in Wiener Space

TL;DR: In this paper, asymptotic bounds for the Gaussian measure of a small ball in terms of the hitting probabilities of a suitably chosen infinite dimensional Brownian motion were provided.
Proceedings ArticleDOI

A Game Theoretic Approach for the Cooperative Network with the Presence of Malicious Relays

TL;DR: It is proved, with Rayleigh fading, the optimal strategy for malicious relays is to transmit independent Gaussian noise using full power at each relay and for cooperative relays was to independently re-encode the source's message into Gaussian signals and forward them to the destination.
References
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Book

Stochastic processes

J. L. Doob, +1 more
Journal ArticleDOI

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, +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].