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...

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Veröffentlicht in:Journal of statistical software Jg. 32; H. 5
Hauptverfasser: Leeuw, Jan de, Hornik, Kurt, Mair, Patrick
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Foundation for Open Access Statistics 01.10.2009
Schlagworte:
active set
isotone optimization
monotone regression
PAVA
ISSN:1548-7660, 1548-7660
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Zusammenfassung: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