  The astronomy community has at its disposal a large back catalog of public
spectroscopic galaxy redshift surveys that can be used for the measurement of
luminosity functions. Utilizing the back catalog with new photometric surveys
to maximum efficiency requires modeling the color selection bias imposed on
selection of target galaxies by flux limits at multiple wavelengths. The
likelihood derived herein can address, in principle, all possible color
selection biases through the use of a generalization of the luminosity
function, $\Phi(L)$, over the space of all spectra: the spectro-luminosity
functional, $\Psi[L_\nu]$. It is, therefore, the first estimator capable of
simultaneously analyzing multiple redshift surveys in a consistent way. We also
propose a new way of parametrizing the evolution of the classic Shechter
function parameters, $L_\star$ and $\phi_\star$, that improves both the
physical realism and statistical performance of the model. The techniques
derived in this work will be used in an upcoming paper to measure the
luminosity function of galaxies at the rest frame wavelength of
$2.4\operatorname{\mu m}$ using the Widefield Infrared Survey Explorer (WISE).
