IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v179y2021ics0167715221001723.html
   My bibliography  Save this article

Non-convex isotonic regression via the Myersonian approach

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715221001723
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2021.109210?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Stout, Quentin F., 2008. "Unimodal regression via prefix isotonic regression," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 289-297, December.
    2. Peter L. Jackson & William L. Maxwell & John A. Muckstadt, 1988. "Determining Optimal Reorder Intervals in Capacitated Production-Distribution Systems," Management Science, INFORMS, vol. 34(8), pages 938-958, August.
    3. Ait-Sahalia, Yacine & Duarte, Jefferson, 2003. "Nonparametric option pricing under shape restrictions," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 9-47.
    4. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-180, January.
    5. Toikka, Juuso, 2011. "Ironing without control," Journal of Economic Theory, Elsevier, vol. 146(6), pages 2510-2526.
    6. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
    7. Paul Glasserman & Jeremy Staum, 2003. "Resource Allocation Among Simulation Time Steps," Operations Research, INFORMS, vol. 51(6), pages 908-921, December.
    8. Ravindra K. Ahuja & James B. Orlin, 2001. "A Fast Scaling Algorithm for Minimizing Separable Convex Functions Subject to Chain Constraints," Operations Research, INFORMS, vol. 49(5), pages 784-789, October.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Alex Gershkov & Benny Moldovanu & Philipp Strack & Mengxi Zhang, 2021. "A Theory of Auctions with Endogenous Valuations," Journal of Political Economy, University of Chicago Press, vol. 129(4), pages 1011-1051.
    2. Ostrizek, Franz & Sartori, Elia, 2023. "Screening while controlling an externality," Games and Economic Behavior, Elsevier, vol. 139(C), pages 26-55.
    3. Hu, Audrey & Offerman, Theo & Zou, Liang, 2011. "Premium auctions and risk preferences," Journal of Economic Theory, Elsevier, vol. 146(6), pages 2420-2439.
    4. Hernandez-Chanto, Allan & Fioriti, Andres, 2019. "Bidding securities in projects with negative externalities," European Economic Review, Elsevier, vol. 118(C), pages 14-36.
    5. Kotowski, Maciej H., 2018. "On asymmetric reserve prices," Theoretical Economics, Econometric Society, vol. 13(1), January.
    6. Feess, Eberhard & Grund, Christian & Walzl, Markus & Wohlschlegel, Ansgar, 2020. "Competing trade mechanisms and monotone mechanism choice," European Journal of Operational Research, Elsevier, vol. 280(3), pages 1108-1121.
    7. Che,Y.-K. & Kim,J., 2001. "Know thy enemies : knowledge of rivals' types and its effect on auctions," Working papers 9, Wisconsin Madison - Social Systems.
    8. Li, Yunan, 2019. "Efficient mechanisms with information acquisition," Journal of Economic Theory, Elsevier, vol. 182(C), pages 279-328.
    9. Mylovanov, Tymofiy & Tröger, Thomas, 2008. "Optimal Auction Design and Irrelevance of Private Information," Bonn Econ Discussion Papers 21/2008, University of Bonn, Bonn Graduate School of Economics (BGSE).
    10. Chade, Hector & Schlee, Edward E., 2020. "Insurance as a lemons market: Coverage denials and pooling," Journal of Economic Theory, Elsevier, vol. 189(C).
    11. Noldeke,G. & Samuelson,L., 2004. "Decomposable principal-agent problems," Working papers 14, Wisconsin Madison - Social Systems.
    12. Levent Ülkü, 2013. "Optimal combinatorial mechanism design," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 53(2), pages 473-498, June.
    13. Noldeke, Georg & Samuelson, Larry, 2007. "Optimal bunching without optimal control," Journal of Economic Theory, Elsevier, vol. 134(1), pages 405-420, May.
    14. Nozomu Muto & Yasuhiro Shirata & Takuro Yamashita, 2020. "Revenue-Capped Efficient Auctions," Journal of the European Economic Association, European Economic Association, vol. 18(3), pages 1284-1320.
    15. Sun, Wuqin & Wang, Dazhong & Zhang, Yue, 2018. "Optimal profit sharing mechanisms with type-dependent outside options," Journal of Mathematical Economics, Elsevier, vol. 75(C), pages 57-66.
    16. Yingkai Li, 2021. "Selling Data to an Agent with Endogenous Information," Papers 2103.05788, arXiv.org, revised Aug 2023.
    17. Dirk Bergemann & Alessandro Bonatti & Alex Smolin, 2018. "The Design and Price of Information," American Economic Review, American Economic Association, vol. 108(1), pages 1-48, January.
    18. L. Elisa Celis & Gregory Lewis & Markus Mobius & Hamid Nazerzadeh, 2014. "Buy-It-Now or Take-a-Chance: Price Discrimination Through Randomized Auctions," Management Science, INFORMS, vol. 60(12), pages 2927-2948, December.
    19. Alejandro Francetich, 2023. "When partner knows best: asymmetric expertise in partnerships," International Journal of Game Theory, Springer;Game Theory Society, vol. 52(2), pages 363-399, June.
    20. Chen, Jiakai, 2021. "LIBOR's poker," Journal of Financial Markets, Elsevier, vol. 55(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:179:y:2021:i:c:s0167715221001723. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.