adopting different statistical approaches for a subsample of UGSs. Finally, conclusions are presented in Section \[sec:summary\].

The sample selection {#sec:sample}
====================

To build our association procedure we considered a sample of blazars selected from the combination of the ROMA-BZCAT [@massaro09; @massaro10] and the 2FGL [@abdo11], as described and used in Paper II and used in Paper III to parametrize the [[*WGS*]{}]{}, denoted the 2FB sample. It contains 284 $\gamma$-ray blazars (135 BZBs and 149 BZQs) that have optical and radio counterparts as reported in the ROMA-BZCAT, and also having a [[*WISE*]{}]{} counterpart within 2.4 $^{\prime\prime}$ radius (see Paper I and III). The blazars in the 2FB sample are detected by [[*WISE*]{}]{} with a signal to noise ratio higher than 7 in at least one band and do not have any upper limits in all the [[*WISE*]{}]{} bands. We excluded from our analysis all the blazars with a [[*Fermi*]{}]{} analysis flag, according to the 2FGL and the 2LAC [@abdo11; @ackermann11a]. The blazars of uncertain type (BZUs) have been excluded from our analysis, while the BL Lac candidates have been considered as BZBs. More details on the 2FB sample and the source selections are given in Papers II and III.

Then, we 