Enhancing Hotelling's T2 Statistic using Shrinkage Covariance Matrix for Identifying Differentially Expressed Gene Sets

The breakthrough of microarray technology is a vital research instrument to measure the quantitative and highly parallel of gene expression. In microarray studies, it is common that the data set typically consists of tens of thousands of genes (variables) from just dozens of samples due to various constraints including the high cost of producing microarray chips. As a result, the combined sample covariance matrix in Hotelling’s T statistic is not invertible. Therefore the distribution of the resulting statistic is either unknown or insufficient. In this study, shrinkage covariance matrix is proposed to improve Hotelling’s T statistic for identification of differentially expressed gene sets. The use of shrinkage covariance matrix overcomes the non-singularity problem in the estimation of sample covariance matrix when the number of variables is larger than the number of samples. The performance of the proposed method was measured using simulation study. The result implies that this approach outperforms existing techniques in many conditions tested.