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Exact Nonparametric Two-Sample Homogeneity Tests for Possibly Discrete Distributions


  • DUFOUR, Jean-Marie
  • FARHAT, Abdeljelil


In this paper, we study several tests for the equality of two unknown distributions. Two are based on empirical distribution functions, three others on nonparametric probability density estimates, and the last ones on differences between sample moments. We suggest controlling the size of such tests (under nonparametric assumptions) by using permutational versions of the tests jointly with the method of Monte Carlo tests properly adjusted to deal with discrete distributions. We also propose a combined test procedure, whose level is again perfectly controlled through the Monte Carlo test technique and has better power properties than the individual tests that are combined. Finally, in a simulation experiment, we show that the technique suggested provides perfect control of test size and that the new tests proposed can yield sizeable power improvements.

Suggested Citation

  • DUFOUR, Jean-Marie & FARHAT, Abdeljelil, 2001. "Exact Nonparametric Two-Sample Homogeneity Tests for Possibly Discrete Distributions," Cahiers de recherche 2001-23, Universite de Montreal, Departement de sciences economiques.
  • Handle: RePEc:mtl:montde:2001-23

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    References listed on IDEAS

    1. Kiviet, Jan F. & Dufour, Jean-Marie, 1997. "Exact tests in single equation autoregressive distributed lag models," Journal of Econometrics, Elsevier, vol. 80(2), pages 325-353, October.
    2. Dufour, Jean-Marie & Torres, Olivier, 2000. "Markovian processes, two-sided autoregressions and finite-sample inference for stationary and nonstationary autoregressive processes," Journal of Econometrics, Elsevier, vol. 99(2), pages 255-289, December.
    3. Dufour, Jean-Marie, 2006. "Monte Carlo tests with nuisance parameters: A general approach to finite-sample inference and nonstandard asymptotics," Journal of Econometrics, Elsevier, vol. 133(2), pages 443-477, August.
    4. G. Noether, 1963. "Note on the kolmogorov statistic in the discrete case," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 7(1), pages 115-116, December.
    5. Dufour, Jean-Marie, 1990. "Exact Tests and Confidence Sets in Linear Regressions with Autocorrelated Errors," Econometrica, Econometric Society, vol. 58(2), pages 475-494, March.
    6. Jean-Marie Dufour & Abdeljelil Farhat & Lucien Gardiol & Lynda Khalaf, 1998. "Simulation-based finite sample normality tests in linear regressions," Econometrics Journal, Royal Economic Society, vol. 1(Conferenc), pages 154-173.
    7. Dufour, Jean-Marie, 1989. "Nonlinear Hypotheses, Inequality Restrictions, and Non-nested Hypotheses: Exact Simultaneous Tests in Linear Regressions," Econometrica, Econometric Society, vol. 57(2), pages 335-355, March.
    8. Jean-Marie Dufour & Jan F. Kiviet, 1998. "Exact Inference Methods for First-Order Autoregressive Distributed Lag Models," Econometrica, Econometric Society, vol. 66(1), pages 79-104, January.
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    Cited by:

    1. Kidd, Willis V. & Brorsen, B. Wade, 2004. "Why have the returns to technical analysis decreased?," Journal of Economics and Business, Elsevier, vol. 56(3), pages 159-176.

    More about this item


    nonrametric methods; two-same oblem; discrete distribution; discontinuous distribution; goodness-of-fit test; Kolmogorov-Smirnov test; Cramér-von Mises; kernel density estimator; exact test; rmutation test; Monte Carlo test; bootstra combined test ocedure; induced test;

    JEL classification:

    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C50 - Mathematical and Quantitative Methods - - Econometric Modeling - - - General


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