A Comprehensive Statistical Description of Radio-Through-$\gamma$-Ray
  Spectral Energy Distributions of All Known Blazars
  We combined multi-wavelength data for blazars from the Roma-BZCAT catalog and
analyzed hundreds of X-ray spectra. We present the fluxes and Spectral Energy
Distributions (SEDs), in 12 frequency bands from radio to $\gamma$-rays, for a
final sample of 2214 blazars. Using a model-independent statistical approach,
we looked for systematic trends in the SEDs; the most significant trends
involved the radio luminosities and X-ray spectral indices of the blazars. We
used a Principal Component Analysis (PCA), to determine the basis vectors of
the blazar SEDs and, in order to maximize the size of the sample, imputed
missing fluxes using the K-nearest neighbors method. Using more than an order
of magnitude more data than was available when Fossati et al. (1997, 1998)
first reported trends of SED shape with blazar luminosity, we confirmed the
anti-correlation between radio luminosity and synchrotron peak frequency,
although with greater scatter than was seen in the smaller sample. The same
trend can be seen between bolometric luminosity and synchrotron peak frequency.
Finally, we used all available blazar data to determine an empirical SED
description that depends only on the radio luminosity at 1.4~GHz and the
redshift. We verified that this statistically significant relation was not a
result of the luminosity-luminosity correlations that are natural in
flux-limited samples (i.e., where the correlation is actually caused by the
redshift rather than the luminosity).
