Before revision: th eigenvalue is bounded, under the alternative of a change(either in the loadings, or in the number of factors itself) it becomes spiked  . Given that the sample eigenvalue cannot be estimated consistently under the null, we regularise the problem by randomising the test statisticin conjunction with sample conditioning , obtaining a sequence of \textit{i.i.d . , asymptotically chi-square statisticswhich are then employed to build the monitoring scheme.
After revision: th eigenvalue is bounded, under the alternative of a change(either in the loadings, or in the number of factors itself) it becomes spiked . Given that the sample eigenvalue cannot be estimated consistently under the null, we randomise the test statistic , obtaining a sequence of \textit{i.i.d . , asymptotically chi-square statisticswhich are then employed to build the monitoring scheme.