Transformation Methods for Trigonometric Parallaxes

Abstract

The idea of transforming a measured trigonometric parallax to some auxiliary variable when estimating distances and absolute magnitudes was suggested by Smith and Eichhorn in 1996 as a way to avoid the problems of bias and infinite variance with the distance estimates and as an essentially assumption-free alternative to Bayesian and modelling methods. At that time there were three major issues left outstanding: 1) improvement of the transformation for absolute magnitude; 2) satisfactory treatment of the uncertainties when combining estimates from the transformations; and 3) extension of the range of the transformation for distance. Subsequently an additional issue was raised, namely the possible effect of the stellar spatial distribution on the method. The progress made in resolving these issues is discussed, and some comments are made regarding the rôle of transformation methods within the larger framework of distance estimation and the calibration problem.