GCT.test and GCT.sim average these values across $j=1,\dots,p$ to obtain the centering $1 + \hat{a}_{n}/n + \hat{b}_{n}/n^2$ for the generalized component test statistic.center(xy,n,m,ntoorderminus=2)n + m containing the concatenation of the n realizations of a given component from the first sample and the m realizations of the same component from the second sample.
xy belonging to the first sample.xy belonging to the second sample.ntoorderminus=0, then $1$ is returned. If ntoorderminus=1 then $1 + \hat{c}_{jn}/n$ is returned. If ntoorderminus=2 then $1 + \hat{c}_{jn}/n+\hat{d}_{jn}/n^2 $ is returned.ntoorderminus=0,1,2.