Isotonic Regression under Lipschitz Constraint

L. Yeganova () and W. J. Wilbur ()
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L. Yeganova: National Institutes of Health
W. J. Wilbur: National Institutes of Health

Journal of Optimization Theory and Applications, 2009, vol. 141, issue 2, No 12, 429-443

Abstract: 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.

Keywords: Isotonic regression; Lipschitz continuous function; PAV algorithm (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-008-9477-0

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