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 : “ff 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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     title = {Goodness of fit test for isotonic regression},
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     language = {en},
     url = {http://www.numdam.org/item/PS_2001__5__119_0/}
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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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