The validity of the "Pool-Adjacent-Violator" algorithm

M. Martin Diaz and B. Salvador González

Statistics & Probability Letters, 1988, vol. 6, issue 3, 143-145

Abstract: 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[greater-or-equal, slanted]0 can be determined through the Pool-Adjacent-Violator (PAV) algorithm if and only if the restrictions cone, Â, is acute. We also show that such a solution can be determined in one step if and only if  is right-angled. In the problem of isotonic regression (see e.g. Barlow and others (1972))  is acute. In the problems studied by Shaked (1979), Dykstra and Robertson (1983),  is right-angled.

Keywords: isotonic; regression; maximum; likelihood; estimation; pool-adjacent-violator; convex; cone; acute; and; right-angled (search for similar items in EconPapers)
Date: 1988
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