ABSTRACT

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.