OPTIMAL GALAXY DISTANCE ESTIMATORS

The statistical properties of galaxy distance estimators corresponding to the Tully-Fisher and D-n-sigma 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 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 utilizing 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. In this illustrative example the optimal distance estimator derived from apparent magnitude, isophotal diameter, and line width has an intrinsic scatter which is similar to 22% smaller than that of the conventional Tully-Fisher relation.