Nuclear starbursts may contribute to the obscuration of active galactic nuclei ( AGNs ) . The predicted star formation rates are modest , and , for the obscured AGNs that form the X-ray background at z < 1 , the associated faint radio emission lies just beyond the sensitivity limits of the deepest surveys . Here , we search for this level of star formation by studying a sample of 359 X-ray selected AGNs at z < 1 from the COSMOS field that are not detected by current radio surveys . The AGNs are separated into bins based on redshift , X-ray luminosity , obscuration , and mid-infrared characteristics . An estimate of the AGN contribution to the radio flux density is subtracted from each radio image , and the images are then stacked to uncover any residual faint radio flux density . All of the bins containing 24 \mu m-detected AGNs are detected with a signal-to-noise > 3 \sigma in the stacked radio images . In contrast , AGNs not detected at 24 \mu m are not detected in the resulting stacked radio images . This result provides strong evidence that the stacked radio signals are likely associated with star formation . The estimated star formation rates derived from the radio stacks range from 3 { M _ { \odot } } yr ^ { -1 } to 29 { M _ { \odot } } yr ^ { -1 } . Although it is not possible to associate the radio emission with a specific region of the host galaxies , these results are consistent with the predictions of nuclear starburst disks in AGN host galaxies .