The impact of observational selection effects on the estimation of cosmological parameters from galaxy redshift surveys is a topic of considerable interest - and some controversy - in cosmology. We present a new, non-parametric, technique for extracting information from galaxy surveys which circumvents a number of problematic issues affecting traditional, parametric, methods. Our ROBUST technique builds on the C-method and allows determination of cosmological parameters free of almost any model assumptions concerning the galaxy luminosity function and spatial clustering. We also describe a related technique which provides a non-parametric test of completeness in flux-limited galaxy surveys. We illustrate ROBUST by estimating the Hubble parameter and linear bias parameter from recent redshift-distance data. We also discuss applications to the study of the galaxy luminosity function and testing the homogeneity of the Universe on large scales.