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Semiparametric inference on the means of multiple nonnegative distributions with excess zero observations

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

Abstract

A non-standard, but not uncommon, situation is to observe multiple samples of nonnegative data which have a high proportion of zeros. This is the so-called excess of zeros situation and this paper looks at the problem of making inferences about the means of the underlying distributions. Under the semiparametric setup, proposed by Wang et al. (2017), we develop a unified inference framework, based on an empirical likelihood ratio (ELR) statistic, for making inferences on the means of multiple such distributions. A chi-square-type limiting distribution of this statistic is established under a general linear null hypothesis about the means. This result allows us to construct a new test for mean equality. Simulation results show favorable performance of the proposed ELR when compared with other existing methods for testing mean equality, especially when the correctly specified basis function in the density ratio model is the logarithm function. A real data set is analyzed to illustrate the advantages of the proposed method.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:166:y:2018:i:c:p:182-197
    DOI: 10.1016/j.jmva.2018.02.010
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    References listed on IDEAS

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    1. Critchley, Frank & Marriott, Paul & Salmon, Mark, 1996. "On the Differential Geometry of the Wald Test with Nonlinear Restrictions," Econometrica, Econometric Society, vol. 64(5), pages 1213-1222, September.
    2. 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.
    3. 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.
    4. Zhou, Xiao-Hua & Tu, Wanzhu, 2000. "Interval estimation for the ratio in means of log-normally distributed medical costs with zero values," Computational Statistics & Data Analysis, Elsevier, vol. 35(2), pages 201-210, December.
    5. 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.
    6. Jing Qin & Han Zhang & Pengfei Li & Demetrius Albanes & Kai Yu, 2015. "Using covariate-specific disease prevalence information to increase the power of case-control studies," Biometrika, Biometrika Trust, vol. 102(1), pages 169-180.
    7. Gupta, Ramesh C. & Li, Xue, 2006. "Statistical inference for the common mean of two log-normal distributions and some applications in reliability," Computational Statistics & Data Analysis, Elsevier, vol. 50(11), pages 3141-3164, July.
    8. Shuwen Wan & Binrong Xu & Biao Zhang, 2016. "Using logistic regression for semiparametric comparison of population means and variances," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(9), pages 2485-2503, May.
    9. Chen, Song Xi & Qin, Jing, 2003. "Empirical likelihood-based confidence intervals for data with possible zero observations," Statistics & Probability Letters, Elsevier, vol. 65(1), pages 29-37, October.
    10. 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. 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.
    2. Zhang, Archer Gong & Chen, Jiahua, 2022. "Density ratio model with data-adaptive basis function," Journal of Multivariate Analysis, Elsevier, vol. 191(C).

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