Estimating the external accuracy of HIPPARCOS parallaxes by deconvolution.

Abstract

The external standard errors of a statistically homogeneous set of trigonometric parallaxes may be estimated from the distribution of small and negative parallax values. The paper describes a method using the Richardson-Lucy deconvolution algorithm combined with a fitting procedure to derive simultaneously an estimate of the distribution of true parallaxes and of the external standard error of observation. Monte Carlo simulations are used to determine the bias and uncertainty of the estimated standard errors. The method is applied to preliminary parallaxes from the ESA Hipparcos mission. The formal standard errors assigned to the preliminary Hipparcos data are found to be in very good agreement with the external estimates obtained with the present method, thus confirming that most of the space parallaxes have external standard errors well below 2mas.