How to Improve Upon t-tests or F-tests for a Large Number of Hypotheses? -By Shrinking Both the Means and Variances

Abstract

In the modern day application of Statistics, we often face the problem of testing a large number of hypotheses. One primary example is microarray experiment, since the number of genes simultaneously studied could easily be as big as ten thousand. The number of observations for each hypothesis testing is however small typically around 6. Tests based on separate observations have poor power and there is a great need to search for alternative more powerful tests by using all the combined observations. Recently the research area of improving upon t-tests or F-tests has become very active. A popular example is SAM proposed by Storey and Tibshirani (2003). The newly proposed test by Cui,Hwang, Qiu, Blades, Churchill (Biostatistics 2005), called Fs test, works very well in power. So do the tests proposed by Wright and Simon (Bioinformatics 2003) and Smyth (SAGMB 2004). When Fs is applied to control FDR, it is also more powerful than the corresponding procedure based on the usual F-test. We focus on finding a theory that explains why Fs does well. This procedure and the two procedures above however only modify or shrink the variances. Should we shrink the means too? Come and find out whether that improve the power further. The talk is based on my joint work with Peng Liu, Cornell University.