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Goodness‐of‐Fit Test for Monotone Functions

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  • CÉCILE DUROT
  • LAURENCE REBOUL

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.

Suggested Citation

  • Cécile Durot & Laurence Reboul, 2010. "Goodness‐of‐Fit Test for Monotone Functions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(3), pages 422-441, September.
    • Handle: RePEc:bla:scjsta:v:37:y:2010:i:3:p:422-441
    DOI: 10.1111/j.1467-9469.2010.00688.x
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    References listed on IDEAS

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    1. Gilles R. Ducharme & Bénédicte Fontez, 2004. "A Smooth Test of Goodness-of-Fit for Growth Curves and Monotonic Nonlinear Regression Models," Biometrics, The International Biometric Society, vol. 60(4), pages 977-986, December.
    2. Fan J. & Huang L-S., 2001. "Goodness-of-Fit Tests for Parametric Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 640-652, June.
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    Cited by:

    1. Colubi, Ana & Domínguez-Menchero, J. Santos & González-Rodríguez, Gil, 2014. "Testing constancy in monotone response models," Computational Statistics & Data Analysis, Elsevier, vol. 72(C), pages 45-56.
    2. Fadoua Balabdaoui, 2014. "Global convergence of the log-concave MLE when the true distribution is geometric," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(1), pages 21-59, March.

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