Goodness‐of‐Fit Test for Monotone Functions

Cécile Durot and Laurence Reboul

Scandinavian Journal of Statistics, 2010, vol. 37, issue 3, 422-441

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 ‐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.

Date: 2010
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https://doi.org/10.1111/j.1467-9469.2010.00688.x

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Persistent link: https://EconPapers.repec.org/RePEc:bla:scjsta:v:37:y:2010:i:3:p:422-441

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