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Goodness of fit test for isotonic regression
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- Journal:
- ESAIM: Probability and Statistics / Volume 5 / 2001
- Published online by Cambridge University Press:
- 15 August 2002, pp. 119-140
- Print publication:
- 2001
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- Article
- Export citation
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We consider the problem of hypothesis testing within a monotoneregression model. We propose a new test of the hypothesisH 0: “ƒ = ƒ0 ” against the composite alternative H a : “ƒ ≠ ƒ0 ” under the assumption that the true regression functionf is decreasing. The test statistic is based on the ${\mathbb L}_{1}$
-distance between the isotonic estimator of f and thefunction f 0, since it is known that a properly centered and normalized version of this distance is asymptotically standardnormally distributed under H 0. We study the asymptotic powerof the test under alternatives that converge to the nullhypothesis.
