Defining extremes and trimming by minimum covering sets
type: Item
instance of: scholarly article
title: Defining extremes and trimming by minimum covering sets
zbMATH Open document ID: 0703.60015
DOI: 10.1016/0304-4149(90)90130-K
published in: Stochastic Processes and their Applications
publication date: 1990-01-01T00:00:00Z
review text: Given a class \(\{\) \(R\}\) of convex subsets of \(R^ d\), the author defines extremes in a d-variate sample as the points of the sample that lie on the boundary of the smallest set R which contains the whole sample. Corresponding trimmed sums are then sums of all sample points omitting layers of the extremes. Representations for the distributions of these trimmed sums are obtained and used to establish necessary and sufficient conditions for consistency and asymptotic normality if the number of points removed remains bounded in probability as the sample size increases. It turns out that, as in the one-dimensional case, this form of light trimming does not improve the asymptotic behavior of the sample mean. The general approach presented in the paper contains as special cases the minimum covering ellipse of a sample and trimming by polyhedra.
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60G50
Mathematics Subject Classification ID: 62G35
zbMATH DE Number: 4153570
zbMATH Keywords: multivariate extremes
zbMATH Keywords: robust location estimator
zbMATH Keywords: sufficient conditions for consistency
zbMATH Keywords: asymptotic normality
author: Ross A. Maller
MaRDI profile type: Publication
cites work: The Extreme Terms of a Sample and Their Role in the Sum of Independent Variables
cites work: Die konvexe H�lle von n rotationssymmetrisch verteilten Punkten
cites work: The asymptotic distribution of trimmed sums
cites work: What portion of the sample makes a partial sum asymptotically stable or normal?
cites work: THE COVERING CIRCLE OF A SAMPLE FROM A CIRCULAR NORMAL DISTRIBUTION
cites work: The convex hull of a random sample in
cites work: The convex hull of a spherically symmetric sample
cites work: Q3968288
cites work: Matrix normalized sums of independent identically distributed random vectors
cites work: The central limit problem for trimmed sums
cites work: Asymptotic normality and subsequential limits of trimmed sums
cites work: Limit theorems for convex hulls
cites work: Q3668396
cites work: Limit theory for multivariate sample extremes
cites work: Matrix normalization of sums of random vectors in the domain of attraction of the multivariate normal
cites work: The multidimensional central limit theorem for arrays normed by affine transformations
cites work: On the Extreme Terms of a Sample From the Domain of Attraction of a Stable Law
cites work: Evaluating inclusion functionals for random convex hulls
cites work: What is Projection Pursuit?
cites work: Q3921896
cites work: Asymptotic normality of lightly trimmed means – a converse
cites work: Asymptotic normality of trimmed means in higher dimensions
cites work: On the limit distributions of lightly trimmed sums
cites work: Q3833334
cites work: Sur L'enveloppe convexe des nuages de points aleatoires dans Rn. I
cites work: Q3825955
cites work: A bivariate stable characterization and domains of attraction
cites work: The probability that two samples in the plane will have disjoint convex hulls
cites work: Q4765784
cites work: Minimum Covering Ellipses
cites work: The asymptotic distribution of the trimmed mean
cites work: Optimal design: Some geometrical aspects of D-optimality
cites work: Estimation of Correlation Coefficients by Ellipsoidal Trimming
cites work: Non-Parametric Estimation II. Statistically Equivalent Blocks and Tolerance Regions--The Continuous Case
cites work: An Extension of Wilks' Method for Setting Tolerance Limits
full work available at URL: 0304-4149(90)90130-k
OpenAlex ID: W2016723951
Recommended article: Q4735203
Recommended article: Extremal problems on sum-free sets and coverings in tridimensional spaces
Recommended article: Covering points with convex sets of minimum size
Recommended article: Covering Points with Convex Sets of Minimum Size
Recommended article: Constructing Minimal Coverability Sets
Recommended article: Q4303878
Recommended article: Q3715127
Recommended article: Extremal problems among subsets of a set
description: scientific article; zbMATH DE number 4153570