The galaxy luminosity function and the Local Hole
  Whitbourn & Shanks (2014) have reported evidence for a local void underdense
by ~15% extending to 150-300h-1Mpc around our position in the Southern Galactic
Cap (SGC). Assuming a local luminosity function they modelled K- and r-limited
number counts and redshift distributions in the 6dFGS/2MASS and SDSS redshift
surveys and derived normalised n(z) ratios relative to the standard homogeneous
cosmological model. Here we test further these results using maximum likelihood
techniques that solve for the galaxy density distributions and the galaxy
luminosity function simultaneously. We confirm the results from the previous
analysis in terms of the number density distributions, indicating that our
detection of the 'Local Hole' in the SGC is robust to the assumption of either
our previous, or newly estimated, luminosity functions. However, there are
discrepancies with previously published K and r band luminosity functions. In
particular the r-band luminosity function has a steeper faint end slope than
the r0.1 results of Blanton et al. (2003) but is consistent with the r0.1
results of Montero-Dorta & Prada (2009); Loveday et al. (2012).
