Two new estimators for the proportion of true null hypotheses in multiple test

ABSTRACT

In multiple hypothesis test, an important problem is estimating the proportion of true null hypotheses. Existing methods are mainly based on the p-values of the single tests. In this paper, we propose two new estimations for this proportion. One is a natural extension of the commonly used methods based on p-values and the other is based on a mixed distribution. Simulations show that the first method is comparable with existing methods and performs better under some cases. And the method based on a mixed distribution can get accurate estimators even if the variance of data is large or the difference between the null hypothesis and alternative hypothesis is very small.

KEYWORDS:

• Multiple hypothesis testing
• proportion of true null hypotheses
• combined p-value method
• method based on a mixed distribution

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The research is supported by the Fundamental Research Funds for the Central Universities, and the Research Funds of Renmin University of China [No. 12XNI004].