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1989•Mathematics of Operations ResearchRequires access

Isotonic Median Regression: A Linear Programming Approach

Nilotpal Chakravarti

Open publisher page 75 citations

Abstract

The isotonic median regression problem arises in statistics. It is known that the isotonic median regression problem, with respect to a complete order, may be solved by a “Pool Adjacent Violators” algorithm. In this paper we show that this algorithm is a dual method for solving a linear programming formulation of the problem. The linear programming approach provides additional insight into the algorithm as well as a simple proof of its validity. We also analyze the computational complexity of the algorithm and discuss its significance from the standpoint of linear programming theory.

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What this paper is about

The isotonic median regression problem arises in statistics. It is known that the isotonic median regression problem, with respect to a complete order, may be solved by a “Pool Adjacent Violators” algorithm. In this paper we show that this algorithm is a dual method for solving a linear programming formulation of the problem. The linear programming approach provides additional insight into the algorithm as well as a simple proof of its validity. We also analyze the computational complexity of the algorithm and discuss its significance from the standpoint of linear programming theory.

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OpenAlex reports 75 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

The isotonic median regression problem arises in statistics. It is known that the isotonic median regression problem, with respect to a complete order, may be solved by a “Pool Adjacent Violators” algorithm. In this paper we show that this algorithm is a dual method for solving a linear programming formulation of the problem. The linear programming approach provides additional insight into the algorithm as well as a simple proof of its validity. We also analyze the computational complexity of the algorithm and discuss its significance from the standpoint of linear programming theory.

Key concepts: Isotonic regression, Mathematics, Linear programming, Isotonic, Linear regression, Mathematical optimization, Simple (philosophy), Linear-fractional programming

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