Microarray technology allows a scientist to study genome-wide patterns of gene expression.Thousands of individual genes are measured with relatively little replication which poses challenges to traditional statistical methods.In particular,the gene-specific estimates of variances are not reliable and gene-by-gene tests have low power.We propose a family of shrinkage estimators for variances raised to a fixed power.We derive optimal shrinkage parameters under both Stein and the squared loss functions.