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Goodness of fit test for isotonic regression
Published online by Cambridge University Press: 15 August 2002
Abstract
We consider the problem of hypothesis testing within a monotone
regression model. We propose a new test of the hypothesis
H0: “ƒ = ƒ0” against the composite alternative Ha: “ƒ ≠ ƒ0” under the assumption that the true regression function
f is decreasing. The test statistic is based on the
${\mathbb L}_{1}$-distance between the isotonic estimator of f and the
function f0, since it is known that a properly centered and
normalized version of this distance is asymptotically standard
normally distributed under H0. We study the asymptotic power
of the test under alternatives that converge to the null
hypothesis.
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- Research Article
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- Copyright
- © EDP Sciences, SMAI, 2001
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