On the estimation of a convex set
type: Item
instance of: scholarly article
title: On the estimation of a convex set
zbMATH Open document ID: 0557.62032
author: Marc Moore
published in: The Annals of Statistics
publication date: 1984-01-01T00:00:00Z
review text: Let \(x_ 1,...,x_ n\) be independent and uniformly distributed on an unknown compact convex set D in \({\mathbb{R}}^ p\) (p known). The author considers the decision-theoretic estimation of the set D when the loss function is \(L(D,\hat D)=m(D\Delta \hat D)\) where \(\hat D\) is the estimate, m the Lebesgue measure and \(D\Delta\) \(\hat D\) is the symmetric difference between D and \(\hat D.\) Under suitable conditions he proves a complete class theorem for Bayes procedures. The cases \(p=1\) and \(p=2\) are discussed in detail, and the consistency of Bayes procedures is established.
reviewed by: Rasul A. Khan
Mathematics Subject Classification ID: 62F15
Mathematics Subject Classification ID: 62F99
Mathematics Subject Classification ID: 60D05
Mathematics Subject Classification ID: 62C07
Mathematics Subject Classification ID: 62C10
zbMATH DE Number: 3888712
zbMATH Keywords: estimation of convex sets
zbMATH Keywords: loss function
zbMATH Keywords: consistency
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1176346725
OpenAlex ID: W2054062606
DOI: 10.1214/AOS/1176346725
description: scientific article; zbMATH DE number 3888712