Non-convex isotonic regression via the Myersonian approach

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 th...

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Veröffentlicht in:Statistics & probability letters 2021-12, Vol.179, p.109210, Article 109210
Hauptverfasser: Cui, Zhenyu, Lee, Chihoon, Zhu, Lingjiong, Zhu, Yunfan
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Sprache:eng
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Zusammenfassung: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.
ISSN:0167-7152
1879-2103
DOI:10.1016/j.spl.2021.109210