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 -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 distributed under . We study the asymptotic power of the test under alternatives that converge to the null hypothesis.
Keywords: nonparametric regression, isotonic estimator, goodness of fit test, asymptotic power
@article{PS_2001__5__119_0, author = {Durot, C\'ecile and Tocquet, Anne-Sophie}, title = {Goodness of fit test for isotonic regression}, journal = {ESAIM: Probability and Statistics}, pages = {119--140}, publisher = {EDP-Sciences}, volume = {5}, year = {2001}, mrnumber = {1875667}, zbl = {0990.62041}, language = {en}, url = {http://www.numdam.org/item/PS_2001__5__119_0/} }
Durot, Cécile; Tocquet, Anne-Sophie. Goodness of fit test for isotonic regression. ESAIM: Probability and Statistics, Volume 5 (2001), pp. 119-140. http://www.numdam.org/item/PS_2001__5__119_0/
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