IDEAS home Printed from https://ideas.repec.org/p/zbw/sfb373/199843.html
   My bibliography  Save this paper

A nonparametric test of the non-convexity of regression

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.econstor.eu/bitstream/10419/61308/1/721976123.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Enno Mammen, "undated". "Comparing nonparametric versus parametric regression fits," Statistic und Oekonometrie 9205, Humboldt Universitaet Berlin.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Tatiana Komarova & Javier Hidalgo, 2019. "Testing nonparametric shape restrictions," Papers 1909.01675, arXiv.org, revised Jun 2020.
    2. 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.
    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Dabo-Niang, Sophie & Francq, Christian & Zakoïan, Jean-Michel, 2010. "Combining Nonparametric and Optimal Linear Time Series Predictions," Journal of the American Statistical Association, American Statistical Association, vol. 105(492), pages 1554-1565.
    2. Bissantz, Nicolai & Holzmann, Hajo, 2007. "Statistical inference for inverse problems," Technical Reports 2007,40, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    3. Richard K. Crump & V. Joseph Hotz & Guido W. Imbens & Oscar A. Mitnik, 2008. "Nonparametric Tests for Treatment Effect Heterogeneity," The Review of Economics and Statistics, MIT Press, vol. 90(3), pages 389-405, August.
    4. Escanciano, Juan Carlos & Jacho-Chávez, David T., 2010. "Approximating the critical values of Cramér-von Mises tests in general parametric conditional specifications," Computational Statistics & Data Analysis, Elsevier, vol. 54(3), pages 625-636, March.
    5. Nicolas Debarsy & Vincenzo Verardi, 2010. "Estimating Nonlinearities in Spatial Autoregressive Models," Working Papers halshs-00446574, HAL.
    6. Juei-Chao Chen, 1994. "Testing for no effect in nonparametric regression via spline smoothing techniques," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(2), pages 251-265, June.
    7. Thomas Triebs & Subal C. Kumbhakar, 2012. "Management Practice in Production," ifo Working Paper Series 129, ifo Institute - Leibniz Institute for Economic Research at the University of Munich.
    8. Limão, Nuno & Handley, Kyle, 2013. "Policy Uncertainty, Trade and Welfare: Theory and Evidence for China and the U.S," CEPR Discussion Papers 9615, C.E.P.R. Discussion Papers.
    9. Poulin, Jennifer & Duchesne, Pierre, 2008. "On the power transformation of kernel-based tests for serial correlation in vector time series: Some finite sample results and a comparison with the bootstrap," Computational Statistics & Data Analysis, Elsevier, vol. 52(9), pages 4432-4457, May.
    10. Mark Fiecas & Hernando Ombao, 2016. "Modeling the Evolution of Dynamic Brain Processes During an Associative Learning Experiment," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(516), pages 1440-1453, October.
    11. Donald W. K. Andrews & Xiaoxia Shi, 2013. "Inference Based on Conditional Moment Inequalities," Econometrica, Econometric Society, vol. 81(2), pages 609-666, March.
    12. repec:cwl:cwldpp:1761rr is not listed on IDEAS
    13. Zhang, Chunming & Dette, Holger, 2003. "A power comparison between nonparametric regression tests," Technical Reports 2003,22, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    14. Pascal Lavergne & Valentin Patilea, 2011. "One for All and All for One: Regression Checks With Many Regressors," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(1), pages 41-52, January.
    15. Zhang, Chun-Xia & Mei, Chang-Lin & Zhang, Jiang-She, 2007. "An empirical study of a test for polynomial relationships in randomly right censored regression models," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6543-6556, August.
    16. Neumann, Michael H. & Paparoditis, Efstathios, 1998. "A nonparametric test for the stationary density," SFB 373 Discussion Papers 1998,58, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    17. Anatolyev Stanislav, 2019. "Testing for a Functional Form of Mean Regression in a Fully Parametric Environment," Journal of Econometric Methods, De Gruyter, vol. 8(1), pages 1-20, January.
    18. Duchesne, Pierre & Li, Linyuan & Vandermeerschen, Jill, 2010. "On testing for serial correlation of unknown form using wavelet thresholding," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2512-2531, November.
    19. Oliver Linton & Kyungchui (Kevin) Song & Yoon-Jae Whang, 2008. "Bootstrap tests of stochastic dominance with asymptotic similarity on the boundary," CeMMAP working papers CWP08/08, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    20. Dette, Holger & Hetzler, Benjamin, 2004. "Specification tests indexed by bandwidths," Technical Reports 2004,48, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    21. Härdle, Wolfgang & Sperlich, Stefan & Spokoiny, Vladimir G., 1997. "Component analysis for additive models," SFB 373 Discussion Papers 1997,52, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:zbw:sfb373:199843. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ZBW - Leibniz Information Centre for Economics (email available below). General contact details of provider: https://edirc.repec.org/data/sfhubde.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.