Bias and variance reduction in estimating the proportion of true-null hypotheses

Yebin Cheng, Dexiang Gao, Tiejun TONG*

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

9 Citations (Scopus)
32 Downloads (Pure)


When testing a large number of hypotheses, estimating the proportion of true nulls, denoted by π0, becomes increasingly important. This quantity has many applications in practice. For instance, a reliable estimate of π0 can eliminate the conservative bias of the Benjamini-Hochberg procedure on controlling the false discovery rate. It is known that most methods in the literature for estimating π0 are conservative. Recently, some attempts have been paid to reduce such estimation bias. Nevertheless, they are either over bias corrected or suffering from an unacceptably large estimation variance. In this paper, we propose a new method for estimating π0 that aims to reduce the bias and variance of the estimation simultaneously. To achieve this, we first utilize the probability density functions of false-null p-values and then propose a novel algorithm to estimate the quantity of π0. The statistical behavior of the proposed estimator is also investigated. Finally, we carry out extensive simulation studies and several real data analysis to evaluate the performance of the proposed estimator. Both simulated and real data demonstrate that the proposed method may improve the existing literature significantly.

Original languageEnglish
Pages (from-to)189-204
Number of pages16
Issue number1
Publication statusPublished - 1 Jan 2015

Scopus Subject Areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

User-Defined Keywords

  • Effect size
  • False-null p-value
  • Microarray data
  • Multiple testing
  • Probability density function
  • Upper tail probability


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