Goodness-of-Fit Test for Monotone Functions

نویسندگان

  • CÉCILE DUROT
  • LAURENCE REBOUL
چکیده

In this article, we develop a test for the null hypothesis that a real-valued function belongs to a given parametric set against the non-parametric alternative that it is monotone, say decreasing. The method is described in a general model that covers the monotone density model, the monotone regression and the right-censoring model with monotone hazard rate. The criterion for testing is an L p-distance between a Grenander-type non-parametric estimator and a parametric estimator computed under the null hypothesis. A normalized version of this distance is shown to have an asymptotic normal distribution under the null, whence a test can be developed. Moreover, a bootstrap procedure is shown to be consistent to calibrate the test.

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تاریخ انتشار 2010