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Isotonic Regression under Lipschitz Constraint

Author

Listed:
  • L. Yeganova

    (National Institutes of Health)

  • W. J. Wilbur

    (National Institutes of Health)

Abstract

The pool adjacent violators (PAV) algorithm is an efficient technique for the class of isotonic regression problems with complete ordering. The algorithm yields a stepwise isotonic estimate which approximates the function and assigns maximum likelihood to the data. However, if one has reasons to believe that the data were generated by a continuous function, a smoother estimate may provide a better approximation to that function. In this paper, we consider the formulation which assumes that the data were generated by a continuous monotonic function obeying the Lipschitz condition. We propose a new algorithm, the Lipschitz pool adjacent violators (LPAV) algorithm, which approximates that function; we prove the convergence of the algorithm and examine its complexity.

Suggested Citation

  • L. Yeganova & W. J. Wilbur, 2009. "Isotonic Regression under Lipschitz Constraint," Journal of Optimization Theory and Applications, Springer, vol. 141(2), pages 429-443, May.
    • Handle: RePEc:spr:joptap:v:141:y:2009:i:2:d:10.1007_s10957-008-9477-0
    DOI: 10.1007/s10957-008-9477-0
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    Cited by:

    1. Nishanth Dikkala & Greg Lewis & Lester Mackey & Vasilis Syrgkanis, 2020. "Minimax Estimation of Conditional Moment Models," Papers 2006.07201, arXiv.org.
    2. 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.

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