Goodness of fit test for isotonic regression

We consider the problem of hypothesis testing within a monotone regression model. We propose a new test of the hypothesis H 0 : “ ƒ = ƒ 0 ” against the composite alternative H a : “ ƒ ≠ ƒ 0 ” under the assumption that the true regression function f is decreasing. The test statistic is based on the -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.

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