  The possibility of a correlation between the radio (cm)- and $\gamma$-ray
luminosity of variable AGN seen by EGRET is investigated. We performed
Monte-Carlo simulations of typical data sets and applied different correlation
techniques (partial correlation analysis, $\chi^2$-test applied on flux-flux
relations) in view of a truncation bias caused by sensitivity limits of the
surveys. For K-corrected flux densities, we find that with the least squares
method only a linear correlation can be recovered. Partial correlation analysis
on the other side provides a robust tool to detect correlations even in
flux-limited samples if intrinsic scatter does not exceed $\sim 40$ \% of the
original $\gamma$-ray luminosity. The analysis presented in this paper takes
into account redshift bias and truncation effects simultaneously which was
never considered in earlier papers.
  Applying this analysis to simultaneously observed radio- and $\gamma$-ray
data, no correlation is found. However, an artificial correlation appears when
using the mean flux. This is probably due to the reduction of the dynamical
range in the flux-flux relation. Furthermore, we show that comparing the
emission in both spectral bands at a high activity state leads to no convincing
correlation.
  In conclusion, we can not confirm a correlation between radio and
$\gamma$-ray luminosities of AGN which is claimed in previous works.

Astrophysics