The DNA microarray technologies permit scientists to depict the expression of genes for related samples. This relationship between genes is analysed using Hotelling’s T2 as a multivariate test statistic but the disadvantage of this test, when used in microarray studies is the number of samples is larger than the number of variables. This study discovers the potential of the shrinkage approach to estimate the covariance matrix specifically when the high dimensionality problem happened. Consequently, the sample covariance matrix in Hotelling’s T2 statistic is not positive definite and become singular thus cannot be inverted. In this research, the Hotelling’s T2 statistic is combined with a shrinkage approach as an alternative estimation to estimate the covariance matrix to detect significant gene sets. The multivariate test statistic of classical Hotelling's T2 is used to integrate the correlation when assessing changes in activity level across biological conditions. The performances of the proposed methods were assessed using real data study. Shrinkage covariance matrix approach indicates a better result for detection of differentially expressed gene sets as compared to other methods.
Robust Hotelling’s T2 statistic based on M-estimator
