Whether a correlation exists between the radio and gamma-ray flux densities of blazars is a long-standing question, and one that is difficult to answer confidently because of various observational biases which may either dilute or apparently enhance
any intrinsic correlation between radio and gamma-ray luminosities. We introduce a novel method of data randomization to evaluate quantitatively the effect of these biases and to assess the intrinsic significance of an apparent correlation between radio and gamma-ray flux densities of blazars. The novelty of the method lies in a combination of data randomization in luminosity space (to ensure that the randomized data are intrinsically, and not just apparently, uncorrelated) and significance assessment in flux space (to explicitly avoid Malmquist bias and automatically account for the limited dynamical range in both frequencies). The method is applicable even to small samples that are not selected with strict statistical criteria. For larger samples we describe a variation of the method in which the sample is split in redshift bins, and the randomization is applied in each bin individually; this variation is designed to yield the equivalent to luminosity-function sampling of the underlying population in the limit of very large, statistically complete samples. We show that for a smaller number of redshift bins, the method yields a worse significance, and in this way it is conservative in that it does not assign a stronger, artificially enhanced significance. We demonstrate how our test performs as a function of number of sources, strength of correlation, and number of redshift bins used, and we show that while our test is robust against common-distance biases and associated false positives for uncorrelated data, it retains the power of other methods in rejecting the null hypothesis of no correlation for correlated data.
We present results from the first two years of our fast-cadence 15 GHz gamma-ray blazar monitoring program, part of the F-GAMMA radio monitoring project. Our sample includes the 1158 blazars north of -20 degrees declination from the Candidate Gamma-R
ay Blazar Survey (CGRaBS), which encompasses a significant fraction of the extragalactic sources detected by the Fermi Gamma-ray Space Telescope. We introduce a novel likelihood analysis for computing a time series variability amplitude statistic that separates intrinsic variability from measurement noise and produces a quantitative error estimate. We use this method to characterize our radio light curves. We also present results indicating a statistically significant correlation between simultaneous average 15 GHz radio flux density and gamma-ray photon flux.
