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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; [email protected].
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; [email protected].
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Abstract

We consider the problem of hypothesis testing within a monotoneregression model. We propose a new test of the hypothesisH 0: “ƒ = ƒ0 ” against the composite alternative H a : “ƒ ≠ ƒ0 ” under the assumption that the true regression functionf is decreasing. The test statistic is based on the ${\mathbb L}_{1}$ -distance between the isotonic estimator of f and thefunction f 0, since it is known that a properly centered and normalized version of this distance is asymptotically standardnormally distributed under H 0. We study the asymptotic powerof the test under alternatives that converge to the nullhypothesis.

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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