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A nonparametric test of the non-convexity of regression

Author

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  • Diack, Cheikh A. T.
  • Thomas-Agnan, Christine

Abstract

This paper proposes a nonparametric test of the non-convexity of a smooth regression function based on least squares or hybrid splines. By a simple formulation of the convexity hypothesis in the class of all polynomial cubic splines, we build a test which has an asymptotic size equal to the nominal level. It is shown that the test is consistent and is robust to nonnormality. The behavior of the test under the local alternatives is studied.

Suggested Citation

  • Diack, Cheikh A. T. & Thomas-Agnan, Christine, 1998. "A nonparametric test of the non-convexity of regression," SFB 373 Discussion Papers 1998,43, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    • Handle: RePEc:zbw:sfb373:199843
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    References listed on IDEAS

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    1. Enno Mammen, "undated". "Comparing nonparametric versus parametric regression fits," Statistic und Oekonometrie 9205, Humboldt Universitaet Berlin.
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    1. Diack, Cheikh A. T., 1998. "A consistent nonparametric test of the convexity of regression based on least squares splines," SFB 373 Discussion Papers 1998,44, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    2. Tatiana Komarova & Javier Hidalgo, 2019. "Testing nonparametric shape restrictions," Papers 1909.01675, arXiv.org, revised Jun 2020.
    3. Hervé Cardot, 2002. "Local roughness penalties for regression splines," Computational Statistics, Springer, vol. 17(1), pages 89-102, March.
    4. Nanjing Jian & Shane G. Henderson, 2020. "Estimating the Probability that a Function Observed with Noise Is Convex," INFORMS Journal on Computing, INFORMS, vol. 32(2), pages 376-389, April.
    5. Komarova, Tatiana & Hidalgo, Javier, 2023. "Testing nonparametric shape restrictions," LSE Research Online Documents on Economics 121410, London School of Economics and Political Science, LSE Library.

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    More about this item

    Keywords

    least squares estimator; test of convexity; B-splines; modulus of continuity;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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