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Tree based diagnostic procedures following a smooth test of goodness-of-fit

Author

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  • Gilles R. Ducharme

    (Université de Montpellier)

  • Walid Al Akhras

    (Université de Montpellier)

Abstract

This paper introduces a statistical procedure, to be applied after a goodness-of-fit test has rejected a null model, that provides diagnostic information to help the user decide on a better model. The procedure goes through a list of departures, each being tested by a local smooth test. The list is organized into a hierarchy by seeking answers to the questions “Where is the problem?” and “What is the problem there?”. This hierarchy allows to focus on finer departures as the data becomes more abundant. The procedure controls the family-wise Type 1 error rate. Simulations show that the procedure can succeed in providing useful diagnostic information.

Suggested Citation

  • Gilles R. Ducharme & Walid Al Akhras, 2016. "Tree based diagnostic procedures following a smooth test of goodness-of-fit," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(8), pages 971-989, November.
    • Handle: RePEc:spr:metrik:v:79:y:2016:i:8:d:10.1007_s00184-016-0585-9
    DOI: 10.1007/s00184-016-0585-9
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    References listed on IDEAS

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    1. Goeman Jelle J. & Finos Livio, 2012. "The Inheritance Procedure: Multiple Testing of Tree-structured Hypotheses," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 11(1), pages 1-18, January.
    2. Norbert Henze, 1997. "Do components of smooth tests of fit have diagnostic properties?," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 45(1), pages 121-130, January.
    3. Nicolai Meinshausen, 2008. "Hierarchical testing of variable importance," Biometrika, Biometrika Trust, vol. 95(2), pages 265-278.
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    Cited by:

    1. Ducharme, Gilles R. & Lafaye de Micheaux, Pierre, 2020. "A goodness-of-fit test for elliptical distributions with diagnostic capabilities," Journal of Multivariate Analysis, Elsevier, vol. 178(C).

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