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Goodness of fit test for isotonic regression

Published online by Cambridge University Press:  15 August 2002

Cécile Durot
Laboratoire de statistiques, bâtiment 425, Université Paris-Sud, 91405 Orsay Cedex, France;
Anne-Sophie Tocquet
Laboratoire Statistique et Génome, 523 place des Terrasses de l'Agora, 91000 Evry, et Département de Mathématiques, Université d'Evry-Val-d'Essonne, boulevard F. Mitterrand, 91025 Evry Cedex, France;
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We consider the problem of hypothesis testing within a monotone regression model. We propose a new test of the hypothesis H0: “ƒ = ƒ0” against the composite alternative Ha: “ƒ ≠ ƒ0” under the assumption that the true regression function f is decreasing. The test statistic is based on the ${\mathbb L}_{1}$-distance between the isotonic estimator of f and the function f0, since it is known that a properly centered and normalized version of this distance is asymptotically standard normally distributed under H0. We study the asymptotic power of the test under alternatives that converge to the null hypothesis.

Research Article
© EDP Sciences, SMAI, 2001

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