Completeness III: identifying characteristic systematics and evolution
  in galaxy redshift surveys
  This paper continues our development of non-parametric tests for analysing
the completeness in apparent magnitude of magnitude-redshift surveys. The
purpose of this third and final paper in our completeness series is two-fold:
firstly we explore how certain forms of incompleteness for a given flux-limited
galaxy redshift survey would manifest themselves in the ROBUST Tc and Tv
completeness estimators introduced in our earlier papers; secondly we provide a
comprehensive error propagation for these estimators. By using both real
surveys and Monte Carlo mock survey data, we have found distinct,
characteristic behaviour of the Tc and Tv estimators which identify
incompleteness in the form of e.g. missing objects within a particular
magnitude range. Conversely we have identified signatures of `over'
completeness, in cases where a survey contains a small region in apparent
magnitude that may have too many objects relative to the rest of the data set.
We also demonstrate how incompleteness resulting from luminosity evolution can
be identified and provide a framework for using our estimators as a robust tool
for constraining models of luminosity evolution.
  Finally we explore the error propagation for Tc andTv. This builds on
Completeness II by allowing the definition of these estimators, and their
errors, via an adaptive procedure that accounts for the effects of sampling
error on the observed distribution of apparent magnitude and redshift in a
survey.
