Validation of our estimator normalization for simulations of the MV reconstruction at the map and power spectrum levels. The map normalization (plotted as ) is tested by taking the cross-spectrum of the input φ with the reconstruction averaged over Monte-Carlo simulations, divided by an f_sky factor to account for missing power in the mask. The power spectrum normalization (plotted as ) is obtained by averaging the first line of Eq. (15)over simulations, and then comparing it to the expected value, which is because our simulations do not contain point-source non-Gaussianity.