The validity of the ``pool-adjacent-violator'' algorithm
type: Item
instance of: scholarly article
title: The validity of the ``pool-adjacent-violator'' algorithm
zbMATH Open document ID: 0633.62028
DOI: 10.1016/0167-7152(88)90109-5
author: M. Martin
author: B. Salvador González
published in: Statistics \& Probability Letters
publication date: 1988-01-01T00:00:00Z
review text: The purpose of this paper is to show that if G is a positive definite symmetric real matrix, the solution to minimize \((g-x)'G(g-x)\) subject to \(x'A\geq 0\) can be determined through the pool-adjacent-violator (PAV) algorithm if and only if the restrictions cone, \(\hat A,\) is acute. We also show that such a solution can be determined in one step if and only if \(\hat A\) is right-angled. In the problem of isotonic regression \(\hat A\) is acute.
Mathematics Subject Classification ID: 62F10
Mathematics Subject Classification ID: 62J02
Mathematics Subject Classification ID: 65C99
zbMATH DE Number: 4030711
zbMATH Keywords: isotonic regression
zbMATH Keywords: maximum likelihood estimation
zbMATH Keywords: convex cone
zbMATH Keywords: pool- adjacent-violator (PAV) algorithm
zbMATH Keywords: right-angled
zbMATH Keywords: acute
MaRDI profile type: Publication
full work available at URL: 0167-7152(88)90109-5
OpenAlex ID: W1988509725
cites work: Q5658961
cites work: Q5563208
cites work: On Testing Monotone Tendencies
description: scientific article; zbMATH DE number 4030711