Non-convex isotonic regression via the Myersonian approach

Zhenyu Cui, Chihoon Lee, Lingjiong Zhu and Yunfan Zhu

Statistics & Probability Letters, 2021, vol. 179, issue C

Abstract: Isotonic regression refers to a class of regression models with order constraints. It is widely used in maximum likelihood estimation of ordered parameter, testing of distributions with ordered means, multistage production systems, and machine learning. A vast majority of the literature considers the isotonic regression problems with convex or piece-wise convex objective functions (or those that can be converted to such functions). We connect a class of isotonic regression problems with the so-called ironing problem in mechanism design, by establishing a discrete version of the Myerson’s ironing method. We use such a connection to solve an isotonic regression problem with non-convex objective functions. We also prove the optimality of pool adjacent violator (PAV) algorithm in such a case.

Keywords: Isotonic regression; PAV algorithm; Myerson’s ironing; Convex hull (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1016/j.spl.2021.109210

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