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Goodness of fit test for isotonic regression

Published online by Cambridge University Press:  15 August 2002

Cécile Durot  and
Anne-Sophie Tocquet
Cécile Durot
Affiliation:
Laboratoire de statistiques, bâtiment 425, Université Paris-Sud, 91405 Orsay Cedex, France; Cecile.Durot@math.u-psud.fr.
Anne-Sophie Tocquet
Affiliation:
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; atocquet@maths.univ-evry.fr.
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Abstract

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.

Keywords

Nonparametric regressionisotonic estimatorgoodness of fit testasymptotic power.
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 5 , 2001 , pp. 119 - 140
Copyright
© EDP Sciences, SMAI, 2001

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