Asymptotics for statistical distances based on Voronoi tessellations
type: Item
instance of: scholarly article
title: Asymptotics for statistical distances based on Voronoi tessellations
zbMATH Open document ID: 1011.62021
DOI: 10.1023/A:1014819112010
published in: Journal of Theoretical Probability
publication date: 2002-08-20T00:00:00Z
review text: The Voronoi tessellation of a set of points \(\{x_1,\ldots,x_n\}\) in \(\mathbb R^d\) is a partition which associates with \(x_i\) the `cell' of all elements of \(\mathbb R^d\) which are closer to \(x_i\) than to any other \(x_j\), \(j\neq i\). The authors obtain an information-type inequality and a strong law for a wide class of statistical distances between empirical estimates and random measures, based on such Voronoi tessellations. Their results extend some basic results in the asymptotic theory of sample spacings, when the Voronoi cells are interpreted as \(d\)-dimensional spacings. The study exploits a monotonicity property of Voronoi tessellations analogous to that found in 1-dimensional spacings.
Mathematics Subject Classification ID: 62E99
Mathematics Subject Classification ID: 60F15
Mathematics Subject Classification ID: 62B10
Mathematics Subject Classification ID: 62H99
zbMATH DE Number: 1784216
zbMATH Keywords: Voronoi tessallations
zbMATH Keywords: statistical distances
zbMATH Keywords: multi-dimensional spacings
zbMATH Keywords: entropy
zbMATH Keywords: phi-divergence
author: Raúl Jiménez
author: J. E. Yukich
reviewed by: M. P. Quine
MaRDI profile type: Publication
full work available at URL: a:1014819112010
OpenAlex ID: W1579479393
description: scientific article; zbMATH DE number 1784216