An optimal procedure for non-parametric elimination of observational cutoff bias in complete samples

Details An optimal procedure for non-parametric elimination of observational cutoff bias in complete samples An optimal procedure for non-parametric elimination of observational cutoff bias in complete samples

Feb 1983

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1983a%26a...118..180n&link_type=abstract

Astronomy and Astrophysics, vol. 118, no. 1, Feb. 1983, p. 180-188.

Statistics

32

Astrometry, Celestial Bodies, Luminosity, Multivariate Statistical Analysis, Nonparametric Statistics, Red Shift, Computerized Simulation, Distribution Functions, Galactic Radiation, Maximum Likelihood Estimates, Optimization

Scientific paper

An essentially nonparametric, statistically efficient, sufficient, and unbiased estimate of the luminosity function of the objects observed in a complete sample is given. The method applies to multivariate observations, for example of luminosities at several frequencies, and to samples subjected to progressive incompleteness, if known. It consists in taking the values of the differential luminosity function for a binned presentation of the population as unknown parameters, to be estimated by the method of maximum likelihood. This is found to have a unique and explicit solution that is identical with the result of an intuitive and recursive procedure well adapted to computation. Aspects of the procedure, including its insensitivity to binning within reasonable limits, are illustrated by its application to recent complete low-redshift galaxies. Comparison of the results based on the Hubble and Lundmark laws shows the latter clearly fitting more closely.

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