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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 ≠ 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...

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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