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Goodness‐of‐Fit Test for Monotone Functions
Authors:CÉCILE DUROT  LAURENCE REBOUL
Institution:1. Département de Mathématiques, Université Paris‐Sud;2. Département de Mathématiques, Université de Poitiers
Abstract:Abstract. 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 inline image‐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.
Keywords:bootstrap  composite hypothesis  least concave majorant  monotone density  monotone hazard rate  monotone regression  non  parametric alternatives
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