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

• Main Authors: Mair, Patrick, Hornik, Kurt, de Leeuw, Jan
• Format: Others
• Language: en
• Published: American Statistical Association 2009
• Subjects: isotone optimization / PAVA / monotone regression / active set / R
• Online Access: http://epub.wu.ac.at/3993/1/isotone.pdf

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 then 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. (authors' abstract)