JSM 2005 - Toronto

Abstract #303474

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Legend: = Applied Session, = Theme Session, = Presenter
Activity Number: 62
Type: Contributed
Date/Time: Sunday, August 7, 2005 : 4:00 PM to 5:50 PM
Sponsor: Biometrics Section
Abstract - #303474
Title: Why Does Shrinking the Variance Estimates Helps the Multiple Testing for a Large Number of Populations Such as Genes?
Author(s): Peng Liu*+ and J. T. Gene Hwang
Companies: Cornell University and Cornell University
Address: 301 Malott Hall, Ithaca, NY, 14853, United States
Keywords: microarray ; high dimenstion and low sample size ; power ; Fs-test ; pooled variance ; asymptotics
Abstract:

In many experiments such as microarray, the number of populations (genes) is large and sample size for each population is small. Consequently, the variance estimates are unstable. Small variance inflates the test statistics for standard t test and produces false positives. Several statistical tests, including Regularized-t test (Baldi and Long 2001), B-statistics (Lonnstedt and Speed 2002) and Fs-test (Cui et al. 2005), have been proposed to alleviate the problem. In particular, Fs-test is constructed for each gene with a variance estimate that borrows strength from all other genes using the concept of James-Stein shrinkage. Numerical studies show Fs test has nearly the best power when comparing to F-tests using individual variance or pooled variance (Cui et al. 2005). The striking result calls for a theoretical explanation. We study the asymptotic power of Fs-test when the number of genes is large, typically more than than 10,000 for microarray experiments. The asymptotic calculation does explain and support the numerical result and may suggest new ways to develop test statistics for microarray or other high-dimensional data.

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