Estimating the Proportion of True Null Hypotheses Using the Pattern of Observedp-values.
Estimating the proportion of true null hypotheses, π0, has attracted much attention in the recent statistical literature. Besides its apparent relevance for a set of specific scientific hypotheses, an accurate estimate of this parameter is key for many multiple testing procedures. Most existing methods for estimating π0in the literature are motivated from the independence assumption of test statistics, which is often not true in reality. Simulations indicate that most existing estimators in the presence of the dependence among test statistics can be poor, mainly due to the increase of variation in these estimators. In this paper, we propose several data-driven methods for estimating π0by incorporating the distribution pattern of the observedp-values as a practical approach to address potential dependence among test statistics. Specifically, we use a linear fit to give a data-driven estimate for the proportion of true-nullp-values in (λ, 1] over the whole range [0, 1] instead of using the expected proportion at 1 - λ. We find that the proposed estimators may substantially decrease the variance of the estimated true null proportion and thus improve the overall performance.
Department of Mathematics, Hong Kong Baptist University, Hong Kong ; Institute of Computational and Theoretical Studies, Hong Kong Baptist University, Hong Kong.
Tiejun
T
Tong
Zeny
Z
Feng
Julia S
JS
Hilton
Hongyu
H
Zhao
gene expression data; multiple testing; p-value; proportion of true null hypotheses