Quotation de Leeuw, Jan and Hornik, Kurt and Mair, Patrick. 2009. Isotone Optimization in R: Pool-Adjacent-Violators Algorithm (PAVA) and Active Set Methods. Journal of Statistical Software 32 (5): S. 1-24.




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.


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Publication's profile

Status of publication Published
Affiliation WU
Type of publication Journal article
Journal Journal of Statistical Software
Citation Index SCI
WU-Journal-Rating new FIN-A
Language English
Title Isotone Optimization in R: Pool-Adjacent-Violators Algorithm (PAVA) and Active Set Methods
Volume 32
Number 5
Year 2009
Page from 1
Page to 24
URL http://www.jstatsoft.org/v32/i05
DOI http://dx.doi.org/10.18637/jss.v032.i05


Hornik, Kurt (Details)
Mair, Patrick (Former researcher)
de Leeuw, Jan
Institute for Statistics and Mathematics IN (Details)
Research Institute for Computational Methods FI (Details)
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