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.
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Communicated by P.M. Pardalos.
The authors were supported by the Intramural Research Program of NIH, National Library of Medicine.
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Yeganova, L., Wilbur, W.J. Isotonic Regression under Lipschitz Constraint. J Optim Theory Appl 141, 429–443 (2009). https://doi.org/10.1007/s10957-008-9477-0
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DOI: https://doi.org/10.1007/s10957-008-9477-0