ar X iv : a st ro - p h / 93 10 02 9 v 1 1 4 O ct 1 99 3 Optimal Galaxy Distance Estimators

The statistical properties of galaxy distance estimators corresponding to the Tully-Fisher and D n − σ relations are studied, and a rigorous framework for identifying and removing the effects of Malmquist bias due to observational selection is developed. The prescription of Schechter (1980) for defining unbiased distance estimators is verified and extended to more general – and more realistic – cases. Finally, the derivation of 'optimal' unbiased estimators of minimum dispersion, by utilising information from additional suitably correlated observables, is discussed and the results applied to a calibrating sample from the Fornax cluster, as used in the Mathewson spiral galaxy redshift survey. The optimal distance estima-tor derived from apparent magnitude, diameter and 21cm line width has an intrinsic scatter which is 25 % smaller than that of the Tully-Fisher relation for this calibrating sample.