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Estimating the proportion of true null hypotheses, with application to DNA microarray data
Author(s) -
Langaas Mette,
Lindqvist Bo Henry,
Ferkingstad Egil
Publication year - 2005
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/j.1467-9868.2005.00515.x
Subject(s) - estimator , statistics , nonparametric statistics , null hypothesis
Summary. We consider the problem of estimating the proportion of true null hypotheses, π 0 , in a multiple‐hypothesis set‐up. The tests are based on observed p ‐values. We first review published estimators based on the estimator that was suggested by Schweder and Spjøtvoll. Then we derive new estimators based on nonparametric maximum likelihood estimation of the p ‐value density, restricting to decreasing and convex decreasing densities. The estimators of π 0 are all derived under the assumption of independent test statistics. Their performance under dependence is investigated in a simulation study. We find that the estimators are relatively robust with respect to the assumption of independence and work well also for test statistics with moderate dependence.