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).

Revised to reflect MNRAS published version (corrected typos, references, formatting). 13 pages, 16 figures. Plot data is available at the following location: https://sites.google.com/site/jrwhitbourn/publications/