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Exact Nonparametric Two-Sample Homogeneity Tests for Possibly Discrete Distributions

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  • DUFOUR, Jean-Marie
  • FARHAT, Abdeljelil

Abstract

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.

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Bibliographic Info

Paper provided by Universite de Montreal, Departement de sciences economiques in its series Cahiers de recherche with number 2001-23.

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Length: 32 pages
Date of creation: 2001
Date of revision:
Handle: RePEc:mtl:montde:2001-23

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Keywords: 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;

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  1. Dufour, J.-M., 1986. "Nonlinear hypotheses, inequality restrictions and non-nested hypotheses: Exact simultaneous tests in linear regressions," CORE Discussion Papers 1986016, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. DUFOUR, Jean-Marie, 2005. "Monte Carlo Tests with Nuisance Parameters: A General Approach to Finite-Sample Inference and Nonstandard Asymptotics," Cahiers de recherche 03-2005, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  3. Dufour, J.M. & Kiviet, J.F., 1995. "Exact Tests in Single Equation Autoregressive Distributed Lag Models," Cahiers de recherche 9549, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  4. Dufour, J.M. & Torres, O., 2000. "Markovian Progresses, Two-Sided Autoregressions and Finite-Sample Inference for Stationary and Nonstationary Autoregressive Processes," Cahiers de recherche 2000-12, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  5. Dufour, J.M. & Kiviet, J.F., 1995. "Exact Inference Methods for First-Order Autoregressive Distributed Lag Models," Cahiers de recherche 9547, Universite de Montreal, Departement de sciences economiques.
  6. Dufour, J.-M., 1986. "Exact tests and confidence sets in linear regressions with autocorrelated errors," CORE Discussion Papers 1986037, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  7. 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 C154-C173.
  8. G. Noether, 1963. "Note on the kolmogorov statistic in the discrete case," Metrika, Springer, vol. 7(1), pages 115-116, December.
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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.

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