IDEAS home Printed from https://ideas.repec.org/a/bla/scjsta/v37y2010i3p422-441.html
   My bibliography  Save this article

Goodness‐of‐Fit Test for Monotone Functions

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.1467-9469.2010.00688.x
    Download Restriction: no
    File URL: https://libkey.io/10.1111/j.1467-9469.2010.00688.x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    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.
    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. 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.
    2. 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.

    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. Dette, Holger & Marchlewski, Mareen, 2007. "A test for the parametric form of the variance function in apartial linear regression model," Technical Reports 2007,26, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    2. Mason David M. & Eubank Randy, 2012. "Moderate deviations and intermediate efficiency for lack-of-fit tests," Statistics & Risk Modeling, De Gruyter, vol. 29(2), pages 175-187, June.
    3. Bodhisattva Sen & Mary Meyer, 2017. "Testing against a linear regression model using ideas from shape-restricted estimation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(2), pages 423-448, March.
    4. Cui, Xia & Lu, Ying & Peng, Heng, 2017. "Estimation of partially linear regression models under the partial consistency property," Computational Statistics & Data Analysis, Elsevier, vol. 115(C), pages 103-121.
    5. Gao, Jiti & King, Maxwell, 2003. "Estimation and model specification testing in nonparametric and semiparametric econometric models," MPRA Paper 11989, University Library of Munich, Germany, revised Feb 2006.
    6. Teran Hidalgo, Sebastian J. & Wu, Michael C. & Engel, Stephanie M. & Kosorok, Michael R., 2018. "Goodness-of-fit test for nonparametric regression models: Smoothing spline ANOVA models as example," Computational Statistics & Data Analysis, Elsevier, vol. 122(C), pages 135-155.
    7. Masamune Iwasawa, 2015. "A Joint Specification Test for Response Probabilities in Unordered Multinomial Choice Models," Econometrics, MDPI, vol. 3(3), pages 1-31, September.
    8. Xu Guo & Wangli Xu & Lixing Zhu, 2015. "Model checking for parametric regressions with response missing at random," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(2), pages 229-259, April.
    9. 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.
    10. Ngai Sze Han & Shiqing Ling, 2017. "Goodness-Of-Fit Test For Nonlinear Time Series Models," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 12(02), pages 1-21, June.
    11. Wang-Li Xu & Li-Xing Zhu, 2008. "Goodness-of-fit testing for varying-coefficient models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 68(2), pages 129-146, September.
    12. Escanciano, Juan Carlos & Mayoral, Silvia, 2010. "Data-driven smooth tests for the martingale difference hypothesis," Computational Statistics & Data Analysis, Elsevier, vol. 54(8), pages 1983-1998, August.
    13. Jun Bi & Yongxing Wang & Shuai Sun & Wei Guan, 2018. "Predicting Charging Time of Battery Electric Vehicles Based on Regression and Time-Series Methods: A Case Study of Beijing," Energies, MDPI, vol. 11(5), pages 1-18, April.
    14. Qiang Xia & Kejun He & Cuizhen Niu, 2017. "A Model-Adaptive Test for Parametric Single-Index Time Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(6), pages 981-999, November.
    15. Akdeniz Duran, Esra & Härdle, Wolfgang Karl & Osipenko, Maria, 2012. "Difference based ridge and Liu type estimators in semiparametric regression models," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 164-175.
    16. Hairu Wang & Zhiping Lu & Yukun Liu, 2023. "Score test for missing at random or not under logistic missingness models," Biometrics, The International Biometric Society, vol. 79(2), pages 1268-1279, June.
    17. Bratati Chakraborty & Sabyasachi Bhattacharya & Ayanendranath Basu & Subhadip Bandyopadhyay & Amit Bhattacharjee, 2014. "Goodness-of-fit testing for the Gompertz growth curve model," METRON, Springer;Sapienza Università di Roma, vol. 72(1), pages 45-64, April.
    18. Barrientos, Andrés F. & Canale, Antonio, 2021. "A Bayesian goodness-of-fit test for regression," Computational Statistics & Data Analysis, Elsevier, vol. 155(C).
    19. Olivier Lopez & Valentin Patilea, 2007. "Nonparametric Lack-of-fit Tests for Parametric Mean-Regression Model with Censored Data," Working Papers 2007-01, Center for Research in Economics and Statistics.
    20. Viatcheslav Melas & Andrey Pepelyshev & Petr Shpilev & Luigi Salmaso & Livio Corain & Rosa Arboretti, 2015. "On the optimal choice of the number of empirical Fourier coefficients for comparison of regression curves," Statistical Papers, Springer, vol. 56(4), pages 981-997, November.

    More about this item

    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:bla:scjsta:v:37:y:2010:i:3:p:422-441. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0303-6898 .

    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.