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The Two-Sample Problem with Regression Errors : An Empirical Process Approach

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  • Mora, Juan
  • Neumeyer, Natalie

Abstract

We describe how to test the null hypothesis that errors from two parametrically specified regression models have the same distribution versus a general alternative. First we obtain the asymptotic properties of teststatistics derived from the difference between the two residual-based empirical distribution functions. Under the null distribution they are not asymptotically distribution free and, hence, a consistent bootstrap procedure is proposed to compute critical values. As an alternative, we describe how to perform the test with statistics based on martingale-transformed empirical processes, which are asymptotically distribution free. Some Monte Carlo experiments are performed to compare the behaviour of all statistics with moderate sample sizes.

Suggested Citation

  • Mora, Juan & Neumeyer, Natalie, 2005. "The Two-Sample Problem with Regression Errors : An Empirical Process Approach," Technical Reports 2005,05, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    • Handle: RePEc:zbw:sfb475:200505
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    References listed on IDEAS

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    1. Michael G. Akritas & Ingrid Van Keilegom, 2001. "Non‐parametric Estimation of the Residual Distribution," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(3), pages 549-567, September.
    2. Winfried Stute & Li‐Xing Zhu, 2002. "Model Checks for Generalized Linear Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(3), pages 535-545, September.
    3. 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.
    4. Bai, Jushan & Ng, Serena, 2001. "A consistent test for conditional symmetry in time series models," Journal of Econometrics, Elsevier, vol. 103(1-2), pages 225-258, July.
    5. Jushan Bai, 2003. "Testing Parametric Conditional Distributions of Dynamic Models," The Review of Economics and Statistics, MIT Press, vol. 85(3), pages 531-549, August.
    6. Koul, H. L. & Sen, P. K., 1985. "On a Kolmogorov-Smirnov type aligned test in linear regression," Statistics & Probability Letters, Elsevier, vol. 3(3), pages 111-115, June.
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    Cited by:

    1. Juan Mora & Alicia Pérez-Alonso, 2009. "Specification tests for the distribution of errors in nonparametric regression: a martingale approach," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(4), pages 441-452.
    2. Pardo-Fernández, Juan Carlos, 2007. "Comparison of error distributions in nonparametric regression," Statistics & Probability Letters, Elsevier, vol. 77(3), pages 350-356, February.
    3. 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.

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