|Shrinkage Techniques in Microarray Data Analysis
| Tiejun Tong , Ph.D.
Department of Applied Mathematics, University of Colorado-Boulder
April 14, 2008
The development of microarray technology has revolutionized biomedical research,
and microarrays have become a standard tool in biological studies. Due to the cost
and/or other experimental difficulties, it is common that thousands of genes are measured
only with a small number of replicates. In particular, the standard gene-specific estimators
for means and variances are unreliable and the corresponding tests usually have low
power. Shrinkage technique has a long history starting with the amazing inadmissibility
results of the sample mean and the sample variance. To ensure the non-singularity of
the sample covariance matrix, most existing research requires the sample size is larger
than the dimension of the data and thus is not applicable for microarray data directly. In
this talk, I will introduce several shrinkage estimators proposed for high-dimensional data
with low sample sizes, followed by some shrinkage-based test statistics. Simulations and real data analysis show that the proposed shrinkage-based methods provide a powerful and robust approach for detecting differentially expressed genes.