  The statistical properties of galaxy distance estimators are studied and a
rigorous framework is developed for identifying and removing the effects of
Malmquist bias due to obsevational selection. The prescription of Schechter
(1980) for defining unbiased distance estimators is extended to more general --
and more realistic -- cases. The derivation of `optimal' unbiased distance
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 estimator derived from I-band
magnitude, diameter and 21cm line width has an intrinsic scatter which is 25 \%
smaller than that of the Tully-Fisher relation quoted for this calibrating
sample. (Figures are available on request).
