Abstract
In this article the sufficient conditions for the merge and chop of domain partition sets during the computation for isotonic regressions are derived. The proposed merge-and-chop procedure yields exact isotonic regressions in finite steps when the orderings are of Type I or II defined in this paper. Simple tree orderings, umbrella orderings and simple orderings are of Type I or II. The paper also provides an example showing that the procedure works beyond Types I and II orderings.
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