Oracle and Adaptive Compound Decision Rules
for False Discovery Rate Control
J. American Statistical Association 102, 901-912, (2007).Wenguang Sun and Tony Cai
Oracle and Adaptive Compound Decision Rules
for False Discovery Rate Control
J. American Statistical Association 102, 901-912, (2007).Wenguang Sun and Tony Cai
- Abstract: We develop a compound decision theory framework for multiple testing problems and derive an oracle rule based on the z-values that minimizes the false non-discovery rate (FNR) subject to a constraint on the false discovery rate (FDR). It is shown that many commonly used multiple testing procedures, which are p-value based, are inefficient. An adaptive procedure based on the z-values is proposed. It is shown that the z-value based adaptive procedure asymptotically attains the performance of the z-value oracle procedure and is more efficient than the conventional p-value based methods. Numerical performance of the adaptive procedure is investigated using both simulated and real data. In particular our method is demonstrated in an analysis of the microarray data from a HIV study that involves testing a large number of hypotheses simultaneously.
- Paper: pdf file.
- R codes for the adaptive testing procedure. Here is the readme file.
- Other related paper:
- Sun, W. and Cai, T. (2009).
Large-Scale Multiple Testing under Dependency.
Journal of the Royal Statistical Society, Series B 71, 393-424.Cai, T., Jin, J. & Low, M. (2007).
Estimation and confidence sets for sparse normal mixtures.
The Annals of Statistics 35, 2421-2449.Jin, J. & Cai, T. (2007).
Estimating the null and the proportion of non-null effects in large-scale multiple comparisons.
J. American Statistical Association 102, 495-506.