Goodness of fit test for isotonic regression

Durot, Cécile; Tocquet, Anne-Sophie

Durot, Cécile ; Tocquet, Anne-Sophie

ESAIM: Probability and Statistics, Tome 5 (2001), pp. 119-140.

Résumé

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 $H_{a}$ : “ $f \neq f_{0}$ ” 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.

MR Zbl

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},
     journal = {ESAIM: Probability and Statistics},
     pages = {119--140},
     publisher = {EDP-Sciences},
     volume = {5},
     year = {2001},
     mrnumber = {1875667},
     zbl = {0990.62041},
     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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