Shrinkage estimation of covariance matrix in hotelling’s T2 for differentially expressed gene sets / Suryaefiza Karjanto

The microarray technology performs simultaneous analysis of thousands of
genes in a massively parallel manner in one experiment, hence providing
valuable knowledge on gene interaction and function. The understanding
of microarray data has led to the development of new methods in statistics
such as detection of differentially expressed genes. The microarray analysis
was first employed for individual or single gene, but recently it has been
applied to a gene set or a group of the gene. The relationship between genes
in gene set is analysed using Hotelling’s T2 as a multivariate test statistic.
However, the test cannot be applied when the number of samples is larger
than the number of variables which is uncommon in the microarray. Since
the microarray dataset typically consists of tens of thousands of genes from
just dozens of samples due to various constraints, the sample covariance
matrix is not positive definite and singular, thus it cannot be inverted.
Thus, in this study, we proposed shrinkage approaches to estimating the
covariance matrix in Hotelling’s T2 particularly to cater high dimensionality
problem in microarray data. The Hotelling’s T2 statistic was combined
with the shrinkage approach as an alternative estimation to estimate the
covariance matrix in detect significant gene sets. The proposed shrinkage
estimation approach is about taking a weighted average of the sample
covariance matrix and a structured matrix or shrinkage target as shrinkage
of the sample covariance matrix towards a target matrix of the same
dimensions while the shrinkage intensity is the weight that the shrinkage
target receives. Three shrinkage covariance methods were proposed in this
study and are referred as ShrinkA, ShrinkB and ShrinkC..