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

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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≠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
Keywords: 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},
     journal = {ESAIM: Probability and Statistics},
     pages = {119--140},
     publisher = {EDP-Sciences},
     volume = {5},
     year = {2001},
     mrnumber = {1875667},
     zbl = {0990.62041},
     language = {en},
     url = {http://geodesic.mathdoc.fr/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://geodesic.mathdoc.fr/item/PS_2001__5__119_0/