is constructed according to eq. (6) of ref. [@Crocce11b].

For the bootstrap method, we consider $N_{sub} \,=\, 47$ sub-samples and we resample as in [@Norberg]: $N_{r} \,=\, 3 N_{sub}$, ($N_{r}$ is the number of random sub-samples with replacement from the original set) then we generate an amount of 100 bootstrap samples. The error bars are calculated using the covariance matrix, constructed following Norberg et al. (2009) [@Norberg].

As already reported in the literature [@Crocce11a; @Crocce11b; @Norberg], the error bars for the 2PACF are over-estimated by the jackknife and bootstrap error estimators, as compared with the analytical covariance matrix error calculation. In figure \[fig6\] we compare the error bars obtained from diverse estimators, where one can observe that the jackknife and bootstrap methods actually over-estimate the errors of the 2PACF. The black dots represent the error bars estimated directly from the $N=16$ random catalogues, that is, as the standard deviation from the set of 2PACF obtained with each one of these random catalogues.

![ Comparison of the diverse error estimation methods. The triangles representing the non-linear theory approach were slightly shifted to the right side. []{data-label="fig6"}](figure6){width="10.8cm" height="7.7cm"}

The Random catalogues
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A crucial part in the robust, and statistically significant, detection 