Analyzing an extension of the isotonic regression problem

In this paper an extension of the classical problem of isotonic regression is first considered. This problem extends the criterion of minimizing convex functions by considering a more general situation. To solve this problem, the max–min formulae are extended by means of the concept of change-level...

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Bibliographic Details
Published in:Metrika 2007-07, Vol.66 (1), p.19-30
Main Authors: Santos, Domínguez-Menchero J, González-Rodríguez, Gil
Format: Article
Language:English
Subjects:
Algorithms
Regression
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Summary:In this paper an extension of the classical problem of isotonic regression is first considered. This problem extends the criterion of minimizing convex functions by considering a more general situation. To solve this problem, the max–min formulae are extended by means of the concept of change-level vector, leading to new formulae and algorithms. Moreover, we will find explicit expressions for every isotonic regression when the solution is not unique by considering both max–min and change-level formulae. An immediate implication from the considered extension is that bounds for isotonic regressions can be stated. Furthermore, the problem of finding solutions within a horizontal band in the plane can now be solved. Finally, some practical applications are discussed.
ISSN:0026-1335
1435-926X
DOI:10.1007/s00184-006-0084-5