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A strong law of large numbers for simultaneously testing parameters of Lancaster bivariate distributions

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  • Chen, Xiongzhi

Abstract

We prove a strong law of large numbers for simultaneously testing parameters of a large number of dependent, Lancaster bivariate random variables with infinite supports, and discuss its implications.

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  • Chen, Xiongzhi, 2020. "A strong law of large numbers for simultaneously testing parameters of Lancaster bivariate distributions," Statistics & Probability Letters, Elsevier, vol. 167(C).
    • Handle: RePEc:eee:stapro:v:167:y:2020:i:c:s0167715220302145
    DOI: 10.1016/j.spl.2020.108911
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    References listed on IDEAS

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    1. Art B. Owen, 2005. "Variance of the number of false discoveries," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(3), pages 411-426, June.
    2. Armin Schwartzman & Xihong Lin, 2011. "The effect of correlation in false discovery rate estimation," Biometrika, Biometrika Trust, vol. 98(1), pages 199-214.
    3. Chen, Xiongzhi & Doerge, R.W., 2020. "A strong law of large numbers related to multiple testing normal means," Statistics & Probability Letters, Elsevier, vol. 159(C).
    4. Angelo Koudou, 1998. "Lancaster bivariate probability distributions with Poisson, negative binomial and gamma margins," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 7(1), pages 95-110, June.
    5. Chen, Xiongzhi, 2019. "Uniformly consistently estimating the proportion of false null hypotheses via Lebesgue–Stieltjes integral equations," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 724-744.
    6. John D. Storey & Jonathan E. Taylor & David Siegmund, 2004. "Strong control, conservative point estimation and simultaneous conservative consistency of false discovery rates: a unified approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(1), pages 187-205, February.
    7. David Azriel & Armin Schwartzman, 2015. "The Empirical Distribution of a Large Number of Correlated Normal Variables," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(511), pages 1217-1228, September.
    8. Alessio Farcomeni, 2007. "Some Results on the Control of the False Discovery Rate under Dependence," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 34(2), pages 275-297, June.
    9. Gontscharuk, Veronika & Finner, Helmut, 2013. "Asymptotic FDR control under weak dependence: A counterexample," Statistics & Probability Letters, Elsevier, vol. 83(8), pages 1888-1893.
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