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Testing homogeneity for multiple nonnegative distributions with excess zero observations

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  • Wang, Chunlin
  • Marriott, Paul
  • Li, Pengfei

Abstract

The question of testing the homogeneity of distributions is studied when there is an excess of zeros in the data. In this situation, the distribution of each sample is naturally characterized by a non-standard mixture of a singular distribution at zero and a positive component. To model the positive components, a semiparametric multiple-sample density ratio model is employed. Under this setup, a new empirical likelihood ratio (ELR) test for homogeneity is developed and a χ2-type limiting distribution of the ELR is proved under the homogeneous null hypothesis. A nonparametric bootstrap procedure is proposed to calibrate the finite-sample distribution of the ELR. It is shown that this bootstrap procedure approximates the null distribution of the ELR test statistic under both the null and alternative hypotheses. Simulation studies show that the bootstrap ELR test has an accurate type I error, is robust to changes of underlying distributions, is competitive to, and sometimes more powerful than, several popular one- and two-part tests. A real data example is used to illustrate the advantage of the proposed test.

Suggested Citation

  • Wang, Chunlin & Marriott, Paul & Li, Pengfei, 2017. "Testing homogeneity for multiple nonnegative distributions with excess zero observations," Computational Statistics & Data Analysis, Elsevier, vol. 114(C), pages 146-157.
  • Handle: RePEc:eee:csdana:v:114:y:2017:i:c:p:146-157
    DOI: 10.1016/j.csda.2017.04.011
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    References listed on IDEAS

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    1. Markus Pauly & Edgar Brunner & Frank Konietschke, 2015. "Asymptotic permutation tests in general factorial designs," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 77(2), pages 461-473, March.
    2. Taylor Sandra & Pollard Katherine, 2009. "Hypothesis Tests for Point-Mass Mixture Data with Application to `Omics Data with Many Zero Values," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 8(1), pages 1-45, February.
    3. Bedrick, Edward J. & Hossain, Anwar, 2013. "Conditional tests for homogeneity of zero-inflated Poisson and Poisson-hurdle distributions," Computational Statistics & Data Analysis, Elsevier, vol. 61(C), pages 99-106.
    4. F. Zou, 2002. "On empirical likelihood for a semiparametric mixture model," Biometrika, Biometrika Trust, vol. 89(1), pages 61-75, March.
    5. Zhang, Biao, 2002. "Assessing Goodness-of-Fit of Generalized Logit Models Based on Case-Control Data," Journal of Multivariate Analysis, Elsevier, vol. 82(1), pages 17-38, July.
    6. Miguel de Carvalho & Anthony C. Davison, 2014. "Spectral Density Ratio Models for Multivariate Extremes," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(506), pages 764-776, June.
    7. Zhou Xiao-Hua & Wanzhu Tu, 1999. "Comparison of Several Independent Population Means When Their Samples Contain Log-Normal and Possibly Zero Observations," Biometrics, The International Biometric Society, vol. 55(2), pages 645-651, June.
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    Cited by:

    1. Wang, Chunlin & Marriott, Paul & Li, Pengfei, 2018. "Semiparametric inference on the means of multiple nonnegative distributions with excess zero observations," Journal of Multivariate Analysis, Elsevier, vol. 166(C), pages 182-197.
    2. Meng Yuan & Chunlin Wang & Boxi Lin & Pengfei Li, 2022. "Semiparametric inference on general functionals of two semicontinuous populations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(3), pages 451-472, June.

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