Nonparametric reconstruction of the cosmic expansion with local
  regression smoothing and simulation extrapolation
  In this work we present a nonparametric approach, which works on minimal
assumptions, to reconstruct the cosmic expansion of the Universe. We propose to
combine a locally weighted scatterplot smoothing method and a
simulation-extrapolation method. The first one (Loess) is a nonparametric
approach that allows to obtain smoothed curves with no prior knowledge of the
functional relationship between variables nor of the cosmological quantities.
The second one (Simex) takes into account the effect of measurement errors on a
variable via a simulation process. For the reconstructions we use as raw data
the Union2.1 Type Ia Supernovae compilation, as well as recent Hubble parameter
measurements. This work aims to illustrate the approach, which turns out to be
a self-sufficient technique in the sense we do not have to choose anything by
hand. We examine the details of the method, among them the amount of
observational data needed to perform the locally weighted fit which will define
the robustness of our reconstruction. In view of our results, we believe that
our proposal offers a promising alternative for reconstructing global trends of
cosmological data when there is little intuition on the relationship between
the variables and we also think it even presents good prospects to generate
reliable mock data points where the original sample is poor.
