Difference between the N-point functions for the high-pass filtered N_side = 64 FFP8 CMB estimates and the corresponding means estimated from 1000 MC simulations. The Stokes parameters Q_r and U_r were locally rotated so that the correlation functions are independent of coordinate frame. The first row shows results for the temperature map, from left to right, results for the 2-point, pseudo-collapsed 3-point, equilateral 3-point and connected rhombic 4-point functions. We note that the lines lie on top of each other. The second row shows results for the 2-point function, from left to right, TQ_r, TU_r, Q_rQ_r, and U_rU_r. The third row shows results for the pseudo-collapsed 3-point function, from left to right, TQ_rQ_r, TU_rU_r, Q_rQ_rQ_r, and U_rU_rU_r, and the fourth row shows results for the equilateral 3-point function, from left to right, TQ_rQ_r, TU_rU_r, Q_rQ_rQ_r, and U_rU_rU_r. The black solid, red triple-dot-dashed, orange dashed, green dot-dashed, and blue long dashed lines correspond to the true, Commander, NILC, SEVEM, and SMICA maps, respectively. The true CMB map was analysed with added noise corresponding to the SMICA component separation method. The shaded dark and light grey regions indicate the 68% and 95% confidence regions, respectively, estimated using SMICA simulations. See Sect. 7.2 for the definition of the separation angle θ.