IDEAS home Printed from https://ideas.repec.org/p/zbw/sfb475/200325.html
   My bibliography  Save this paper

A note on testing symmetry of the error distribution in linear regression models

Author

Listed:
  • Neumeyer, Natalie
  • Dette, Holger
  • Nagel, Eva-Renate

Abstract

In the classical linear regression model the problem of testing for symmetry of the error distribution is considered. The test statistic is a functional of the difference between the two empirical distribution functions of the estimated residuals and their counterparts with opposite signs. The weak convergence of the difference process to a Gaussian process is established. The covariance structure of this process depends heavily on the density of the error distribution, and for this reason the performance of a symmetric wild bootstrap procedure is discussed in asymptotic theory and by means of a simulation study.

Suggested Citation

  • Neumeyer, Natalie & Dette, Holger & Nagel, Eva-Renate, 2003. "A note on testing symmetry of the error distribution in linear regression models," Technical Reports 2003,25, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    • Handle: RePEc:zbw:sfb475:200325
    as

    Download full text from publisher

    File URL: https://www.econstor.eu/bitstream/10419/49365/1/373261837.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Koul, H. L. & Lahiri, S. N., 1994. "On Bootstrapping M-Estimated Residual Processes in Multiple Linear-Regression Models," Journal of Multivariate Analysis, Elsevier, vol. 49(2), pages 255-265, May.
    2. Koziol, James A., 1985. "A note on testing symmetry with estimated parameters," Statistics & Probability Letters, Elsevier, vol. 3(4), pages 227-230, July.
    3. 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)

    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. 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.
    2. Linton, Oliver & Song, Kyungchul & Whang, Yoon-Jae, 2010. "An improved bootstrap test of stochastic dominance," Journal of Econometrics, Elsevier, vol. 154(2), pages 186-202, February.
    3. 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.
    4. Bissantz, Nicolai & Holzmann, Hajo, 2007. "Statistical inference for inverse problems," Technical Reports 2007,40, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    5. 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.
    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. 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.
    8. 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.
    9. Kyle Handley & Nuno Limão, 2013. "Policy Uncertainty, Trade and Welfare: Theory and Evidence for China and the U.S," NBER Working Papers 19376, National Bureau of Economic Research, Inc.
    10. Holger Dette & Natalie Neumeyer & Ingrid Van Keilegom, 2007. "A new test for the parametric form of the variance function in non‐parametric regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(5), pages 903-917, November.
    11. repec:cwl:cwldpp:1761rr is not listed on IDEAS
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. Natalie Neumeyer, 2009. "Smooth Residual Bootstrap for Empirical Processes of Non‐parametric Regression Residuals," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(2), pages 204-228, June.
    17. Dette, Holger & Hetzler, Benjamin, 2004. "Specification tests indexed by bandwidths," Technical Reports 2004,48, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    18. 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.
    19. John W. Galbraith & Simon van Norden, 2008. "The Calibration of Probabilistic Economic Forecasts," CIRANO Working Papers 2008s-28, CIRANO.
    20. Delgado, Miguel A. & Song, Xiaojun, 2018. "Nonparametric tests for conditional symmetry," Journal of Econometrics, Elsevier, vol. 206(2), pages 447-471.
    21. 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.

    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:sfb475:200325. 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.