Isotone Optimization in R : Pool-Adjacent-Violators Algorithm (PAVA) and Active Set Methods

In this paper we give a general framework for isotone optimization. First we discuss a generalized version of the pool-adjacent-violators algorithm (PAVA) to minimize a separable convex function with simple chain constraints. Besides of general convex functions we extend existing PAVA implementation...

Full description

Saved in:
Bibliographic Details
Published in:Journal of statistical software Vol. 32; no. 5
Main Authors: Leeuw, Jan de, Hornik, Kurt, Mair, Patrick
Format: Journal Article
Language:English
Published: Foundation for Open Access Statistics 01.10.2009
Subjects:
active set
isotone optimization
monotone regression
PAVA
ISSN:1548-7660, 1548-7660
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper we give a general framework for isotone optimization. First we discuss a generalized version of the pool-adjacent-violators algorithm (PAVA) to minimize a separable convex function with simple chain constraints. Besides of general convex functions we extend existing PAVA implementations in terms of observation weights, approaches for tie handling, and responses from repeated measurement designs. Since isotone optimization problems can be formulated as convex programming problems with linear constraints we the develop a primal active set method to solve such problem. This methodology is applied on specific loss functions relevant in statistics. Both approaches are implemented in the R package isotone.
ISSN:1548-7660
1548-7660
DOI:10.18637/jss.v032.i05