The Chebyshev center: A multidimensional estimate of location
type: Item
instance of: scholarly article
title: The Chebyshev center: A multidimensional estimate of location
zbMATH Open document ID: 0588.62076
DOI: 10.1016/0378-3758(86)90148-5
author: Edward J. Halteman
published in: Journal of Statistical Planning and Inference
publication date: 1986-01-01T00:00:00Z
review text: In this paper the center of the smallest k-dimensional sphere enclosing a data set, hereinafter called the Chebyshev center, is introduced as a multidimensional measure of location. The distribution of this estimator, which is a multidimensional generalization of the univariate midrange, is derived in the general case and its properties investigated for a host of distributions. The Chebyshev center is shown to be a maximum likelihood estimator for the center of a uniform distribution over a k-sphere and both unbiased and consistent for the multivariate spherical normal distribution and any spherical finite range distribution.
Mathematics Subject Classification ID: 62H12
Mathematics Subject Classification ID: 62H10
zbMATH DE Number: 3945102
zbMATH Keywords: generalized midrange
zbMATH Keywords: covering k-sphere
zbMATH Keywords: spatial data
zbMATH Keywords: Chebyshev center
zbMATH Keywords: multidimensional measure of location
zbMATH Keywords: maximum likelihood estimator
zbMATH Keywords: uniform distribution over a k-sphere
zbMATH Keywords: multivariate spherical normal distribution
zbMATH Keywords: spherical finite range distribution
MaRDI profile type: Publication
full work available at URL: 0378-3758(86)90148-5
OpenAlex ID: W2017886367
cites work: On the spherical surface of smallest radius enclosing a bounded subset of 𝑛-dimensional euclidean space
cites work: THE COVERING CIRCLE OF A SAMPLE FROM A CIRCULAR NORMAL DISTRIBUTION
cites work: Q3285937
cites work: Q5643065
cites work: Q4403557
cites work: On the Distributions of Midrange and Semi-Range in Samples from a Normal Population
cites work: Estimation of the Mean and Standard Deviation by Order Statistics
cites work: Estimation of the Mean and Standard Deviation by Order Statistics. Part II
description: scientific article; zbMATH DE number 3945102