A test for partial correlation with censored astronomical data

A new procedure is presented, which allows, based on Kendall's $\tau$, to test for partial correlation in the presence of censored data. Further, a significance level can be assigned to the partial correlation -- a problem which hasn't been addressed in the past, even for uncensored data. The results of various tests with simulated data are reported. Finally, we apply this newly developed methodology to estimate the influence of selection effects on the correlation between the soft X--ray luminosity and both total and core radio luminosity in a complete sample of Active Galactic Nuclei.