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Homogeneity tests for several Poisson populations

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  • Chiu, Sung Nok
  • Wang, Ling
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    Abstract

    In this paper we compare the size distortions and powers for Pearson's [chi]2-statistic, likelihood ratio statistic LR, score statistic SC and two statistics, which we call UT and VT here, proposed by [Potthoff, R.F., Whittinghill, M., 1966. Testing for homogeneity: II. The Poisson distribution. Biometrika 53, 183-190] for testing the equality of the rates of K Poisson processes. Asymptotic tests and parametric bootstrap tests are considered. It is found that the asymptotic UT test is too conservative to be recommended, while the other four asymptotic tests perform similarly and their powers are close to those of their parametric bootstrap counterparts when the observed counts are large enough. When the observed counts are not large, Monte Carlo simulation suggested that the asymptotic test using SC, LR and UT statistics are discouraged; none of the parametric bootstrap tests with the five statistics considered here is uniformly best or worst, and the asymptotic tests using Pearson's [chi]2 and VT always have similar powers to their bootstrap counterparts. Thus, the asymptotic Pearson's [chi]2 and VT tests have an advantage over all five parametric bootstrap tests in terms of their computational simplicity and convenience, and over the other four asymptotic tests in terms of their powers and size distortions.

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    Bibliographic Info

    Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

    Volume (Year): 53 (2009)
    Issue (Month): 12 (October)
    Pages: 4266-4278

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    Handle: RePEc:eee:csdana:v:53:y:2009:i:12:p:4266-4278

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    Web page: http://www.elsevier.com/locate/csda

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    1. Russell Davidson & James Mackinnon, 2006. "Improving the reliability of bootstrap tests with the fast double bootstrap," Working Papers halshs-00439247, HAL.
    2. Davidson, Russell & MacKinnon, James G., 2006. "The power of bootstrap and asymptotic tests," Journal of Econometrics, Elsevier, Elsevier, vol. 133(2), pages 421-441, August.
    3. Davidson, Russell & MacKinnon, James G., 1999. "The Size Distortion Of Bootstrap Tests," Econometric Theory, Cambridge University Press, vol. 15(03), pages 361-376, June.
    4. Russell Davidson & James G. MacKinnon, 2001. "Bootstrap Tests: How Many Bootstraps?," Working Papers, Queen's University, Department of Economics 1036, Queen's University, Department of Economics.
    5. Ng, H.K.T. & Gu, K. & Tang, M.L., 2007. "A comparative study of tests for the difference of two Poisson means," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 51(6), pages 3085-3099, March.
    6. Davidson, Russell & MacKinnon, James G, 1998. "Graphical Methods for Investigating the Size and Power of Hypothesis Tests," The Manchester School of Economic & Social Studies, University of Manchester, University of Manchester, vol. 66(1), pages 1-26, January.
    7. Saha, Krishna K. & Bilisoly, Roger, 2009. "Testing the homogeneity of the means of several groups of count data in the presence of unequal dispersions," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 53(9), pages 3305-3313, July.
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