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 twofold: first, 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.
This work was initiated by Rauzy and then extended and developed by Johnston, Teodoro & Hendry (Completeness I) and Teodoro, Johnston & Hendry (Completeness II). Here, we seek to consolidate the ideas laid out in these previous papers. In particular, our goal is to provide for the observational community statistical tools that will be more easily applicable to real survey data. 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. Identifying regions of incompleteness (in apparent magnitude) in this way provides a powerful means to e.g. improve weighting schemes for estimating luminosity functions, or for more accurately determining the selection function required to employ measures of galaxy clustering as a cosmological probe.
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 and Tv. 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.