Abstract
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 alternative H a : “ƒ ≠ ƒ 0” under the assumption that the true regression function ƒ is decreasing. The statistic of the test rest on the L 1 -distance between the isotonic estimator of ƒ and the function ƒ 0 in such a way that it 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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