## Abstract

When testing a large number of hypotheses, estimating the proportion of true nulls, denoted by π_{0}, becomes increasingly important. This quantity has many applications in practice. For instance, a reliable estimate of π_{0} 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 π_{0} 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 π_{0} 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 π_{0}. 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 language | English |
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Pages (from-to) | 189-204 |

Number of pages | 16 |

Journal | Biostatistics |

Volume | 16 |

Issue number | 1 |

DOIs | |

Publication status | Published - 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