Goodness of fit test for isotonic regression
ESAIM: Probability and Statistics, Tome 5 (2001), pp. 119-140.

We consider the problem of hypothesis testing within a monotone regression model. We propose a new test of the hypothesis ${H}_{0}$: “$f={f}_{0}$” against the composite alternative ${H}_{a}$: “$f\ne {f}_{0}$” under the assumption that the true regression function $f$ is decreasing. The test statistic is based on the ${𝕃}_{1}$-distance between the isotonic estimator of $f$ and the function ${f}_{0}$, since it is known that a properly centered and normalized version of this distance is asymptotically standard normally distributed under ${H}_{0}$. We study the asymptotic power of the test under alternatives that converge to the null hypothesis.

Classification : 62G08,  62G10,  62G20
Mots clés : nonparametric regression, isotonic estimator, goodness of fit test, asymptotic power
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author = {Durot, C\'ecile and Tocquet, Anne-Sophie},
title = {Goodness of fit test for isotonic regression},
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Durot, Cécile; Tocquet, Anne-Sophie. Goodness of fit test for isotonic regression. ESAIM: Probability and Statistics, Tome 5 (2001), pp. 119-140. http://www.numdam.org/item/PS_2001__5__119_0/

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