A Simulation Study on the Probability of Correct Selection for Large k Populations

Abstract

An increasing number of contemporary datasets are high dimensional. Applications require these datasets be screened (or filtered) to select a subset for further study. Multiple testing is the standard tool in such applications, although alternatives have begun to be explored. In order to assess the quality of selection in these high-dimensional contexts, Cui and Wilson (2008b) proposed two viable methods of calculating the probability that any such selection is correct (PCS). PCS thereby serves as a measure of the quality of competing statistics used for selection. The first simulation study of this article investigates the two PCS statistics of the above article. It shows that in the high-dimensional case PCS can be accurately estimated and is robust under certain conditions. The second simulation study investigates a nonparametric estimator of PCS.

Keywords:

• Bootstrap
• PCS
• Probability of correct selection
• Ranking and selection
• Simulation

Mathematics Subject Classification:

• 62F07

Acknowledgment

We would like to thank Dr. Thomas Girke, Director of the University of California Riverside Bioinformatics Cluster, for the use of their computers for this research.