On Schmidt's V ?m estimator and other estimators of luminosity functions.
Abstract
Schmidt's (1968) estimator, sometimes used to calculate the luminosity function from a complete sample of observed objects, can be generalized naively to the case in which the maximum distance for detection is a function of the direction. Though unbiased, this estimator then does not have minimum variance and, in some cases, is inferior to the classical estimator. The classical estimator, however, is biased when the magnitude boxes are not infinitesimal. A generalization of Schmidt's estimator is proposed which is unbiased and usually superior to both Schmidt's and the classical estimator. Variance formulas and numerical examples are given. The results can be used in combining several catalogs.
 Publication:

The Astrophysical Journal
 Pub Date:
 August 1976
 DOI:
 10.1086/154538
 Bibcode:
 1976ApJ...207..700F
 Keywords:

 Estimators;
 Galactic Radiation;
 Luminous Intensity;
 Quasars;
 Astronomical Catalogs;
 Entire Functions;
 Statistical Analysis;
 Variance (Statistics);
 Astrophysics