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. 2009 May;141(2):429-443.
doi: 10.1007/s10957-008-9477-0. Epub 2009 Jan 7.

Isotonic Regression under Lipschitz Constraint

L Yeganova  1 , W J Wilbur  1
Affiliations

Isotonic Regression under Lipschitz Constraint

L Yeganova et al. J Optim Theory Appl. 2009 May.

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.

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