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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)

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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
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File Function: Fisrt version / Primera version, 2005
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Publisher 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
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Publication status: Published by Ivie
Handle: RePEc:ivi:wpasad:2005-18

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

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This paper has been announced in the following NEP Reports: References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. 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. [Downloadable!] (restricted)
  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 and Swedish Statistical Association, vol. 29(3), pages 535-545. [Downloadable!] (restricted)
  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, 06. [Downloadable!] (restricted)
  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 and Swedish Statistical Association, vol. 28(3), pages 549-567. [Downloadable!] (restricted)
  5. 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. [Downloadable!] (restricted)
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Cited by:
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  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). [Downloadable!]
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