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- Title
Goodness-of-Fit Test for Monotone Functions.
- Authors
Durot, Cécile;; Reboul, Laurence
- 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.
- Subjects
GOODNESS-of-fit tests; MONOTONE operators; MATHEMATICAL functions; REGRESSION analysis; THEORY of distributions (Functional analysis)
- Publication
Scandinavian Journal of Statistics, 2010, Vol 37, Issue 3, p422
- ISSN
0303-6898
- Publication type
Article
- DOI
10.1111/j.1467-9469.2010.00688.x