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Goodness of fit test for isotonic regression

Cécile Durot; Anne-Sophie Tocquet — 2001

ESAIM: Probability and Statistics

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...

On the distance between the empirical process and its concave majorant in a monotone regression framework

Cécile Durot; Anne-Sophie Tocquet — 2003

Annales de l'I.H.P. Probabilités et statistiques

Goodness of fit test for isotonic regression

Cécile Durot; Anne-Sophie Tocquet — 2010

ESAIM: Probability and Statistics

We consider the problem of hypothesis testing within a monotone regression model. We propose a new test of the hypothesis : “” against the composite alternative : “” under the assumption that the true regression function is decreasing. The test statistic is based on the $𝕃_{1}$ -distance between the isotonic estimator of and the function , since it is known that a properly centered and normalized version of this distance is asymptotically standard normally...

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Goodness of fit test for isotonic regression

On the distance between the empirical process and its concave majorant in a monotone regression framework

Goodness of fit test for isotonic regression