Speaker: Zeny Feng, University of Guelph

Title: Estimation of the proportion of true null hypotheses when testing a large number
of hypotheses

Abstract:

When testing a large number of hypotheses, the problem of
estimating the proportion of true null hypotheses, pi_0, is often of
interest. The estimation of pi_0 becomes a common and practical
problem as modern scientific experiments often involve testing
hundreds and thousands of null hypotheses. In this talk, we first
review several widely used estimators based on threshold methods
and nonparametric maximum likelihood estimation of the p-value
density. The current estimators are all derived under the
assumption of independent test statistics. We compare their
performances through simulation studies. In reality, especially in
cDNA microarray data analysis, there is often strong dependence
among test statistics. We propose data-driven estimators for pi_0 by
incorporating the distribution pattern of the observed p-values
without the assumption of independence. We evaluate and
compare our proposed estimators with others through simulation
studies. We also analyze real data for illustration.