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A Backward-Induction Algorithm for Computing the best ConvexContrast of two Bivariate Samples

Müller, D.W.

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Abstract

For real-valued x(1), x(2), ... , x(n) with real-valued "responses"y(1), y(2), ... , y(n) and "scores" s(1), s(2), ... ,s(n) we solve the problem ofcomputing the maximum of C(k) = s(1) I {y(1) 3 k(x(1))}+ ... + s(n) I { ... } over allconvex functions k on the line. The article describes a recursive relation and analgorithm based on it to compute this value and an optimal k in O(n(3)) steps. Fora special choice of scores, max C(k) can be interpreted as a generalized (one-sided)Kolmogorov-Smirnov statistic to test for treatment effect in nonparametric analysisof covariance.

Item Type: Working paper
Place of Publication: Heidelberg
Date Deposited: 09 Jun 2016 08:14
Date: October 1995
Number of Pages: 14
Faculties / Institutes: The Faculty of Mathematics and Computer Science > Department of Applied Mathematics
Subjects: 510 Mathematics
Uncontrolled Keywords: Convex contrast; bivariate sample; backward-induction algorithm; convex function; nonparametric analysis; real-valued response; treatment effect; special choice; recursive relation
Schriftenreihe ID: Beiträge zur Statistik > Beiträge
Additional Information: Erschienen in: Journal of Computational and Graphical Statistics, Sept. 1999
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