IDEAS home Printed from https://ideas.repec.org/p/zbw/sfb475/200042.html
   My bibliography  Save this paper

Nonparametric analysis of covariance

Author

Listed:
  • Dette, Holger
  • Neumeyer, Natalie

Abstract

In the problem of testing the equality of k regression curves from independent samples we discuss three methods using nonparametric estimation techniques of the regression function. The first test is based on a linear combination of estimators for the integrated variance function in the individual samples and in the combined sample. The second approach transfers the classical one-way analysis of variance to the situation of comparing nonparametric curves, while the third test compares the differences between the estimates of the individual regression functions by means of an L2-distance. We prove asymptotic normality of all considered statistics under the null hypothesis local and fixed alternatives with different rates corresponding to the various cases. Additionally consistency of a wild bootstrap version of the tests is established. In contrast to most of the procedures proposed in the literature the methods introduced in this paper are also applicable in the case of different design points in each sample and heteroscedastic errors. A simulation study is conducted to investigate the finite sample properties of the new tests and a comparison with recently proposed and related procedures is performed.

Suggested Citation

  • Dette, Holger & Neumeyer, Natalie, 2000. "Nonparametric analysis of covariance," Technical Reports 2000,42, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
  • Handle: RePEc:zbw:sfb475:200042
    as

    Download full text from publisher

    File URL: https://www.econstor.eu/bitstream/10419/77111/2/2000-42.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Stefanie Biedermann & Holger Dette, 2000. "Testing linearity of regression models with dependent errors by kernel based methods," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 9(2), pages 417-438, December.
    2. W. González-Manteiga & R. Cao, 1993. "Testing the hypothesis of a general linear model using nonparametric regression estimation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 2(1), pages 161-188, December.
    3. Delgado, Miguel A., 1993. "Testing the equality of nonparametric regression curves," Statistics & Probability Letters, Elsevier, vol. 17(3), pages 199-204, June.
    4. Biedermann, Stefanie & Dette, Holger, 2000. "Testing linearity of regression models with dependent errors by kernel based methods," Technical Reports 2000,40, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    5. King, Eileen & Hart, Jeffrey D. & Wehrly, Thomas E., 1991. "Testing the equality of two regression curves using linear smoothers," Statistics & Probability Letters, Elsevier, vol. 12(3), pages 239-247, September.
    6. Alcalá, J. T. & Cristóbal, J. A. & González-Manteiga, W., 1999. "Goodness-of-fit test for linear models based on local polynomials," Statistics & Probability Letters, Elsevier, vol. 42(1), pages 39-46, March.
    Full references (including those not matched with items on IDEAS)

    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. Wenceslao González-Manteiga & Rosa Crujeiras, 2013. "An updated review of Goodness-of-Fit tests for regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 361-411, September.
    2. Miguel A. Delgado & Juan Carlos Escanciano, 2013. "Conditional Stochastic Dominance Testing," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(1), pages 16-28, January.
    3. Dette, Holger & Neumeyer, Natalie, 2000. "Nonparametric comparison of regression curves - an empirical process approach," Technical Reports 2000,62, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    4. Lavergne, Pascal, 2001. "An equality test across nonparametric regressions," Journal of Econometrics, Elsevier, vol. 103(1-2), pages 307-344, July.
    5. Gørgens, Tue, 2002. "Nonparametric comparison of regression curves by local linear fitting," Statistics & Probability Letters, Elsevier, vol. 60(1), pages 81-89, November.
    6. Yatchew, A., 1999. "An elementary nonparametric differencing test of equality of regression functions," Economics Letters, Elsevier, vol. 62(3), pages 271-278, March.
    7. Dette, Holger & Hetzler, Benjamin, 2004. "Specification tests indexed by bandwidths," Technical Reports 2004,48, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    8. Khismatullina, Marina & Vogt, Michael, 2023. "Nonparametric comparison of epidemic time trends: The case of COVID-19," Journal of Econometrics, Elsevier, vol. 232(1), pages 87-108.
    9. Scheike, Thomas H., 2000. "Comparison of non-parametric regression functions through their cumulatives," Statistics & Probability Letters, Elsevier, vol. 46(1), pages 21-32, January.
    10. 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.
    11. Zhang, Rongmao & Chan, Ngai Hang & Chi, Changxiong, 2023. "Nonparametric testing for the specification of spatial trend functions," Journal of Multivariate Analysis, Elsevier, vol. 196(C).
    12. Anouar El Ghouch & Marc G. Genton & Taoufik Bouezmarni, 2013. "Measuring the Discrepancy of a Parametric Model via Local Polynomial Smoothing," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(3), pages 455-470, September.
    13. Bücher, Axel & Dette, Holger & Wieczorek, Gabriele, 2011. "Testing model assumptions in functional regression models," Journal of Multivariate Analysis, Elsevier, vol. 102(10), pages 1472-1488, November.
    14. Hira Koul & Fang Li, 2005. "Testing for Superiority among Two Time Series," Statistical Inference for Stochastic Processes, Springer, vol. 8(2), pages 109-135, September.
    15. Srihera, Ramidha & Stute, Winfried, 2010. "Nonparametric comparison of regression functions," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 2039-2059, October.
    16. Cécile Durot & Piet Groeneboom & Hendrik P. Lopuhaä, 2013. "Testing equality of functions under monotonicity constraints," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 25(4), pages 939-970, December.
    17. Andrea Meilán-Vila & Jean D. Opsomer & Mario Francisco-Fernández & Rosa M. Crujeiras, 2020. "A goodness-of-fit test for regression models with spatially correlated errors," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(3), pages 728-749, September.
    18. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
    19. Biedermann, Stefanie & Dette, Holger, 2001. "Optimal designs for testing the functional form of a regression via nonparametric estimation techniques," Statistics & Probability Letters, Elsevier, vol. 52(2), pages 215-224, April.
    20. Long Feng & Changliang Zou & Zhaojun Wang & Lixing Zhu, 2015. "Robust comparison of regression curves," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(1), pages 185-204, March.

    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:sfb475:200042. 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/isdorde.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.