---------------------------------------- -------------- -------------- -------------- --
                 Jackknife                  2.04$\sigma$   1.61$\sigma$   1.95$\sigma$  
                 Bootstrap                  1.87$\sigma$   1.05$\sigma$   1.41$\sigma$  
               Linear Theory                2.12$\sigma$   1.86$\sigma$   1.81$\sigma$  
             Non-linear Theory              2.12$\sigma$   1.86$\sigma$   1.81$\sigma$  

  : The statistical significance values for different error estimators, for the $N_{b}$ cases studied here. []{data-label="table1"}

Small shifts in the quasars positions {#sec:small_shift}
-------------------------------------

To show that the BAO bump we found is a robust detection we have performed an important test, namely the *small shifts criterium*, proposed by Carvalho et al. 2016 [@Carvalho]. This test consists of performing the 2PACF analyses in modified quasars catalogues, that is, we generate a modified catalogue by slightly perturbing the true angular positions of the quasars. The main goal of this test is to distinguish the BAO bump, which is expected to be robust and, consequently, survive (or be smoothed) under small perturbations in the quasars positions, from those bumps sourced by systematic effects, which should disappear.

With this in mind, we generated 100 modified catalogues by drawing each quasar’s new position from a Gaussian distribution with mean equal to the original position and standard deviation $\sigma_s$, and for each modified catalogue we computed the 2PACF. Our final estimation of the 2PACF for a given scale $\sigma_s$ is the average 