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Exact Nonparametric Two-Sample Homogeneity Tests for Possibly Discrete Distributions

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Author Info
DUFOUR, Jean-Marie
FARHAT, Abdeljelil

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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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Publisher 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
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Handle: RePEc:mtl:montde:2001-23

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Related research
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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Find related papers by JEL classification:
C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation and Testing
C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
C50 - Mathematical and Quantitative Methods - - Econometric Modeling - - - General

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  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. [Downloadable!] (restricted)
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  2. 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 335-55, March. [Downloadable!] (restricted)
  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. [Downloadable!] (restricted)
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  4. DUFOUR, Jean-Marie & FARHAT, Abdeljelil & GARDIOL, Lucien, 1998. "Simulation-Based Finite-Sample Normality Tests in Linear Regressions," Cahiers de recherche 9811, Universite de Montreal, Departement de sciences economiques. [Downloadable!]
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  5. Dufour, Jean-Marie, 1990. "Exact Tests and Confidence Sets in Linear Regressions with Autocorrelated Errors," Econometrica, Econometric Society, vol. 58(2), pages 475-94, March. [Downloadable!] (restricted)
  6. 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. [Downloadable!] (restricted)
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  7. 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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  8. G. Noether, 1963. "Note on the kolmogorov statistic in the discrete case," Metrika, Springer, vol. 7(1), pages 115-116, December. [Downloadable!] (restricted)
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