Reconstructing galaxy fundamental distributions and scaling relations
  from photometric redshift surveys. Applications to the SDSS early-type sample
  Noisy distance estimates associated with photometric rather than
spectroscopic redshifts lead to a mis-estimate of the luminosities, and produce
a correlated mis-estimate of the sizes. We consider a sample of early-type
galaxies from the SDSS DR6 for which both spectroscopic and photometric
information is available, and apply the generalization of the V_max method to
correct for these biases. We show that our technique recovers the true
redshift, magnitude and size distributions, as well as the true size-luminosity
relation. We find that using only 10% of the spectroscopic information randomly
spaced in our catalog is sufficient for the reconstructions to be accurate
within about 3%, when the photometric redshift error is dz = 0.038. We then
address the problem of extending our method to deep redshift catalogs, where
only photometric information is available. In addition to the specific
applications outlined here, our technique impacts a broader range of studies,
when at least one distance-dependent quantity is involved. It is particularly
relevant for the next generation of surveys, some of which will only have
photometric information.
