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Non-convex isotonic regression via the Myersonian approach

Author

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  • Cui, Zhenyu
  • Lee, Chihoon
  • Zhu, Lingjiong
  • Zhu, Yunfan

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.

Suggested Citation

  • Cui, Zhenyu & Lee, Chihoon & Zhu, Lingjiong & Zhu, Yunfan, 2021. "Non-convex isotonic regression via the Myersonian approach," Statistics & Probability Letters, Elsevier, vol. 179(C).
    • Handle: RePEc:eee:stapro:v:179:y:2021:i:c:s0167715221001723
    DOI: 10.1016/j.spl.2021.109210
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    References listed on IDEAS

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