Non-parametric elimination of the observational magnitude cutoff bias

A method of estimating luminosity functions for complete galaxy or quasar samples is given which entirely eliminates the observational magnitude cutoff bias without any parametric or other a priori assumption as to the form of the luminosity function. The resulting estimated luminosity function contains all information in the sample relevant to the true luminosity function, and is maximum-likelihood. The method is readily computerized and representative results are shown. It should be emphasized that what is involved here is estimation on the basis of a prior hypothesis; the formulation or testing of such hypotheses involves additional considerations, not treated here.