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

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Author Info

  • Juan Mora

    ()
    (Universidad de Alicante)

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 test-statistics 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.

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File URL: http://www.ivie.es/downloads/docs/wpasad/wpasad-2005-18.pdf
File Function: Fisrt version / Primera version, 2005
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Bibliographic Info

Paper provided by Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie) in its series Working Papers. Serie AD with number 2005-18.

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Length: 52 pages
Date of creation: May 2005
Date of revision:
Publication status: Published by Ivie
Handle: RePEc:ivi:wpasad:2005-18

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Related research

Keywords: Two-Sample Problem; Residual-Based Empirical Process; Smooth Bootstrap; Martingale Transform;

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References

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  1. 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.
  2. Winfried Stute, 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.
  3. 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.
  4. Michael G. Akritas, 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.
  5. 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. Alicia Pérez Alonso & Juan Mora, 2008. "Specification Tests for the Distribution of Errors in Nonoarametric Regression: A Martingale Approach," Working Papers. Serie AD 2008-11, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  2. Pardo-Fernández, Juan Carlos, 2007. "Comparison of error distributions in nonparametric regression," Statistics & Probability Letters, Elsevier, vol. 77(3), pages 350-356, February.

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