Statistical errors in our proper motion measurements. Blue points represent errors estimated from the dispersion or width of the apparent proper motion distribution of ‘small-size’ galaxies in each bin of the HSC i-band PSF magnitudes. The orange points represent errors estimated from quasars, which are sourced from the SDSS DR14 quasar sample and matched to our catalogue. The green line illustrates the expected trend of the error with a specific flux of the object. The data points of galaxies align nicely with this expectation. The red points represent errors estimated from the quadrature sum of the centroid errors of galaxies in the S82 and HSC catalogues, while the purple points are derived from the centroid errors in the HSC catalogue alone.