Minimax Estimation of Means with Applications to Microarray Data Analysis

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 replications. In particular, the standard gene-specific estimators for means and variances are unreliable and the corresponding tests usually have low power. Contrary to the recent development on improving the estimation of variances, little attention has been paid to improving the estimation of means. In this talk, I will introduce a new family of shrinkage estimators for the mean vector under the assumption of unequal variances. The proposed estimators are proved to be minimax under the quadratic loss function. We also conduct simulations to evaluate the performance of our proposed estimators and construct a shrinkage-based t-like statistic that utilizes information across genes. Both simulation studies and real data analysis have shown that the shrinkage-based test provides a powerful and robust approach to detect differentially expressed genes.

Acknowledgement: This is a joint work with Professor Liang Chen at University of South California and Professor Hongyu Zhao at Yale University.