Correlation between the error bars given by the standard deviation of 100 Monte-Carlo realizations and the error bars given by the standard deviation of 100 simulated realizations resampled out of a single one thanks to the block bootstrap method, with and without GMCA. Left: spectra are those of the Fe Gaussian in our first toy model with a total number of counts corresponding to a 100 ks observation and a line-to-continuum ratio of 5.93 (in the absence of a synchrotron spectrum, this ratio characterizes the norm of the Gaussian and the ratio of 5.93 corresponds to the fourth norm in our previous tests). Right: Monte-Carlo vs. Block bootstrap error bars on the results given by GMCA on our first toy model, for the same duration and ratio. In both cases, we made 100 Monte-Carlo realizations and we used a block bootstrap resampling on ten realizations, 100 times each, for a block length of 78 (cube root of the total number of events) in order to evaluate the influence of the initial realization on a block bootstrap resampling.