Independent determination of the systematic and random errors of the
  proper motions in the PPMXL catalog using quasars
  Using a sample of 117053 quasars identified in the PPMXL catalog, the
systematic errors of the proper motions in the PPMXL catalog are estimated
independently as -2.0 and -2.1 mas yr$^{-1}$ in $\mu_{\alpha}\cos\delta$ and
$\mu_{\delta}$, respectively. For objects with SDSS $r$ magnitude between 16.0
and 21.0 mag and SDSS $g-r$ color between -0.4 and 1.2, there are no obvious
magnitude and color dependence in the systematic errors of the proper motions
in the PPMXL catalog. The random errors of the proper motions in the PPMXL
catalog change from $\sim4.0$ to $\sim8.0$ mas yr$^{-1}$ along with the
increase of the magnitude of the objects. No color dependence in the random
errors of the proper motions in the PPMXL catalog is found. There are obvious
right ascension $\alpha$ dependence of the systematic errors in both components
of the proper motions in the PPMXL catalog. For quasars with declination
$\delta>0$, the systematic errors of $\mu_{\delta}$ in the PPMXL catalog
increase linearly with $\delta$ with a slope of 0.07 mas yr$^{-1}$ deg$^{-1}$.
  For comparison, using a subsample of quasars identified both in the PPMXL and
SDSS DR7 catalogs, the systematic errors of the USNO-SDSS proper motions in the
SDSS DR7 catalog are derived as 0.9 and 0.5 mas yr$^{-1}$ in
$\mu_{\alpha}\cos\delta$ and $\mu_{\delta}$, respectively. There are no obvious
magnitude, color, and $\alpha$ dependence in the systematic errors of the
USNO-SDSS proper motions. For quasars with declination $\delta>0$, the
systematic errors of $\mu_{\delta}$ in the SDSS DR7 catalog increase linearly
with $\delta$ with a slope of 0.03. The random errors of the USNO-SDSS proper
motions change from $\sim2.5$ to $\sim6.0$ mas yr$^{-1}$ along with the change
of the magnitude and color of the objects.
