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

2009/01/01 by Jan de Leeuw, Kurt Hornik, Patrick Mair · 2 citations
Mathematics · Decision Sciences · #Statistical Methods and Inference #Probabilistic and Robust Engineering Design #Advanced Statistical Methods and Models

paper · doi:10.18637/jss.v032.i05

openalex publication_date 2009/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

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 <b>isotone</b>.

Citations

• Nonmetric Multidimensional Scaling: A Numerical Method
• Active set algorithms for isotonic regression; A unifying framework
• A Theorem on Boolean Matrices
• Numerical optimization

Cited by

• Centered Isotonic Regression: Point and Interval Estimation for Dose–Response Studies
• Isotonic regression [wikipedia]

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