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
About:
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
More filters
Posted Content
High-dimensional outlier detection using random projections
TL;DR: A novel random projections-based procedure to detect outliers in Gaussian multivariate data that consists in projecting the data in several one-dimensional subspaces where an appropriate univariate outlier detection method, similar to Tukey's method but with a threshold depending on the initial dimension and the sample size, is applied.
Journal ArticleDOI
Straight-line models in star-shaped mixtures
TL;DR: In this article, normal-theory inferences are validated in part for straight-line models having star-contoured errors, and bounds on level and envelopes for power curves are given for certain ensembles and mixtures of distributions.
Journal ArticleDOI
On stochastic majorization of the eigenvalues of a Wishart matrix
TL;DR: In this paper, the authors studied the behavior of orthogonally invariant acceptance regions when some λ i increase while others decrease, and showed that the behavior depends on Σ only on the eigenvalues of the covariance matrix Σ of a multivariate normal distribution.
Posted Content
Lower functions and Chung's LILs of the generalized fractional Brownian motion
Ran Wang,Yimin Xiao +1 more
TL;DR: In this article, the Chung-type laws of the iterated logarithm of GFBM were derived for sample path properties at 0 and infinity, respectively, by modifying the arguments of Talagrand (1996).
References
More filters
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,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].