We define our base statistics, the SOCS (T sum) and MOCS (T max), as: Tsum=∑i=1nzi2 and Tmax=max(zi2), respectively. It can be shown that T sum is distributed according to the weighted sum of χ12-distributed random variables: Tsum∼∑iλiχ12 where λ i is the i-th eigenvalue of Σ. Its distribution function can be evaluated numerically (see Section Algorithmic details for gene-score calculations for details). To estimate the null distribution of T max we make use of the fact that P[Tmax≥t]=P[max(|zi|)≥t]=1−P(|zi|<t,i=1,2,…n).
