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Isotone Optimization in R: Pool-Adjacent-Violators Algorithm (PAVA) and Active Set Methods

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  • de Leeuw, Jan
  • Hornik, Kurt
  • Mair, Patrick

Abstract

In this paper we give a general framework for isotone optimization. First we discuss a generalized version of the pool-adjacent-violators algorithm (PAVA) to minimize a separable convex function with simple chain constraints. Besides of general convex functions we extend existing PAVA implementations in terms of observation weights, approaches for tie handling, and responses from repeated measurement designs. Since isotone optimization problems can be formulated as convex programming problems with linear constraints we the develop a primal active set method to solve such problem. This methodology is applied on specific loss functions relevant in statistics. Both approaches are implemented in the R package isotone.

Suggested Citation

  • de Leeuw, Jan & Hornik, Kurt & Mair, Patrick, 2009. "Isotone Optimization in R: Pool-Adjacent-Violators Algorithm (PAVA) and Active Set Methods," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 32(i05).
    • Handle: RePEc:jss:jstsof:v:032:i05
    DOI: http://hdl.handle.net/10.18637/jss.v032.i05
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    1. Moro Russ A. & Härdle Wolfgang K. & Schäfer Dorothea, 2017. "Company rating with support vector machines," Statistics & Risk Modeling, De Gruyter, vol. 34(1-2), pages 55-67, June.
    2. Mario V. Wuthrich & Johanna Ziegel, 2023. "Isotonic Recalibration under a Low Signal-to-Noise Ratio," Papers 2301.02692, arXiv.org.
    3. repec:jss:jstsof:39:i06 is not listed on IDEAS
    4. Domínguez-Menchero, J. Santos & Rivera, Javier & Torres-Manzanera, Emilio, 2014. "Optimal purchase timing in the airline market," Journal of Air Transport Management, Elsevier, vol. 40(C), pages 137-143.
    5. Eduardo L. Montoya & Wendy Meiring, 2016. "An F-type test for detecting departure from monotonicity in a functional linear model," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(2), pages 322-337, June.
    6. Jelsema, Casey M. & Peddada, Shyamal D., 2016. "CLME: An R Package for Linear Mixed Effects Models under Inequality Constraints," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 75(i01).
    7. Nagy, Gábor I. & Barta, Gergő & Kazi, Sándor & Borbély, Gyula & Simon, Gábor, 2016. "GEFCom2014: Probabilistic solar and wind power forecasting using a generalized additive tree ensemble approach," International Journal of Forecasting, Elsevier, vol. 32(3), pages 1087-1093.
    8. Bucarey, Víctor & Labbé, Martine & Morales, Juan M. & Pineda, Salvador, 2021. "An exact dynamic programming approach to segmented isotonic regression," Omega, Elsevier, vol. 105(C).
    9. Legrand, Catherine & Munda, Marco & Janssen, P. & Duchateau, L., 2012. "A general class of time-varying coefficients models for right censored data," LIDAM Discussion Papers ISBA 2012041, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    10. Yang, Bill Huajian, 2019. "Resolutions to flip-over credit risk and beyond," MPRA Paper 93389, University Library of Munich, Germany.
    11. Liao, Xiyue & Meyer, Mary C., 2014. "coneproj: An R Package for the Primal or Dual Cone Projections with Routines for Constrained Regression," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 61(i12).
    12. Wojciech Gamrot, 2013. "Maximum likelihood estimation for ordered expectations of correlated binary variables," Statistical Papers, Springer, vol. 54(3), pages 727-739, August.
    13. Mankad, Shawn & Michailidis, George & Banerjee, Moulinath, 2015. "Threshold Value Estimation Using Adaptive Two-Stage Plans in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 67(i03).
    14. Yang, Bill Huajian, 2019. "Monotonic Estimation for Probability Distribution and Multivariate Risk Scales by Constrained Minimum Generalized Cross-Entropy," MPRA Paper 93400, University Library of Munich, Germany.
    15. Chathura Siriwardhana & K. B. Kulasekera & Somnath Datta, 2018. "Flexible semi-parametric regression of state occupational probabilities in a multistate model with right-censored data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 24(3), pages 464-491, July.
    16. Ana Colubi & J. Santos Dominguez-Menchero & Gil Gonzalez-Rodriguez, 2018. "New designs to consistently estimate the isotonic regression," Computational Statistics, Springer, vol. 33(2), pages 639-658, June.
    17. David Conde & Miguel A. Fernández & Cristina Rueda & Bonifacio Salvador, 2021. "Isotonic boosting classification rules," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 15(2), pages 289-313, June.
    18. Johannes Friedrich & Pengcheng Zhou & Liam Paninski, 2017. "Fast online deconvolution of calcium imaging data," PLOS Computational Biology, Public Library of Science, vol. 13(3), pages 1-26, March.
    19. Oleg Burdakov & Oleg Sysoev, 2017. "A Dual Active-Set Algorithm for Regularized Monotonic Regression," Journal of Optimization Theory and Applications, Springer, vol. 172(3), pages 929-949, March.
    20. Fang, Fang & Chen, Yuanyuan, 2019. "A new approach for credit scoring by directly maximizing the Kolmogorov–Smirnov statistic," Computational Statistics & Data Analysis, Elsevier, vol. 133(C), pages 180-194.
    21. Wanke, Peter & Pestana Barros, Carlos & Chen, Zhongfei, 2015. "An analysis of Asian airlines efficiency with two-stage TOPSIS and MCMC generalized linear mixed models," International Journal of Production Economics, Elsevier, vol. 169(C), pages 110-126.
    22. Yu, Tao & Li, Pengfei & Chen, Baojiang & Yuan, Ao & Qin, Jing, 2023. "Maximum pairwise-rank-likelihood-based inference for the semiparametric transformation model," Journal of Econometrics, Elsevier, vol. 235(2), pages 454-469.
    23. Barragán, Sandra & Fernández, Miguel & Rueda, Cristina & Peddada, Shyamal, 2013. "isocir: An R Package for Constrained Inference Using Isotonic Regression for Circular Data, with an Application to Cell Biology," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 54(i04).

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