Abstract
New recursive formulas are obtained for the isotonic regression of a given function, defined on a finite set, with given weight function with respect to the simple ordering on the set. These formulas directly give the isotonic regression without the use of any algorithm. Since isotonic regressions often arise in problems of statistical inference under order restrictions these formulas are found useful. We demonstrate their usefulness through an application to the problem of nonparametric estimation of a distribution function dominating stochastically a known distribution function.
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