as a function of redshift. While we imposed no optical color selection criteria, the quasars generally follow the colors of SDSS quasars except at very low $z$, where the host dominates the colors. Adding an optical color constraint has no leverage on the selection of quasars, as the colors of quasars are indistinguishable from the colors of many LMC stars.

In Figures \[fig:tau-sigma\]–\[fig:KKO9\], we examine the selection spaces used to select the candidates. First, we inspect the $\tau$–$\hat{\sigma}$ variability plane from [@2010ApJ...708..927K] and [@2010ApJ...721.1014M]. [@2010ApJ...708..927K] proposed a narrow and long trapezoidal region to select high purity sample of AGN candidates. Indeed, if we had restricted our variability selection to this region, we would have a yield of 70% at the price of a significant reduction in completeness. In fact, the distribution of the variability parameters of all quasars follows the distribution found by [@2010ApJ...721.1014M] for SDSS quasars, extending outside the [@2010ApJ...708..927K] selection boundaries, particularly for long $\tau$ where there is also increased contamination from irregularly varying stars. The left panel of Figure \[fig:tau-sigma\] shows the distribution of objects classified as non-quasars (PNe, YSOs, etc.) or where we failed to classify the spectrum in this variability plane. We note that the 