COSMOGRAIL: the COSmological MOnitoring of GRAvItational Lenses XI.
  Techniques for time delay measurement in presence of microlensing
  Measuring time delays between the multiple images of gravitationally lensed
quasars is now recognized as a competitive way to constrain the cosmological
parameters, and it is complementary with other cosmological probes. This
requires long and well sampled optical light curves of numerous lensed quasars,
such as those obtained by the COSMOGRAIL collaboration. High-quality data from
our monitoring campaign call for novel numerical techniques to robustly measure
the delays, as well as the associated random and systematic uncertainties, even
in the presence of microlensing variations. We propose three different point
estimators to measure time delays, which are explicitly designed to handle
light curves with extrinsic variability. These methods share a common
formalism, which enables them to process data from n-image lenses. Since the
estimators rely on significantly contrasting ideas, we expect them to be
sensitive to different bias sources. For each method and data set, we
empirically estimate both the precision and accuracy (bias) of the time delay
measurement using simulated light curves with known time delays that closely
mimic the observations. Finally, we test the self-consistency of our approach,
and we demonstrate that our bias estimation is serviceable. These new methods,
including the empirical uncertainty estimator, will represent the standard
benchmark for analyzing the COSMOGRAIL light curves.
