Step-Down diagnostic analysis for monitoring the covariance matrix of bivariate normal processes

A comparison among VMIX, VMAX and the adapted step-down Sullivan et al. (SE) tests for covariance matrix under bivariate normal assumption is presented. The type I error and power estimates were obtained by using Monte Carlo simulation under different scenarios with respect to covariance and correlation structures. In general, VMIX was more powerful than VMAX being SE more powerful than both, with few exceptions. SE test is more general since it can be used for normal and non-normal data, with no restriction with respect to the pattern of the covariance matrix shifts, and for larger dimension than the bivariate case.