Galaxy rotation curves using a non-parametric regression method: core,
  cusp and fuzzy scalar field dark matter models
  We present a non-parametric reconstruction of the rotation curves (RC) for 88
spiral galaxies under the LOESS+SIMEX technique. In order to compare methods we
also perform the parametric approach assuming core and cuspy dark matter (DM)
profiles: PISO, NFW, Burkert, Spano, the soliton and two fuzzy soliton$+$NFW.
As result of this two approaches, a comparison of the RC obtained is carried
out by computing the distance between central curves and the distance between
1$\sigma$ error bands. Furthermore, we perform a model selection according to
two statistical criteria, the BIC and the value of $\chi^2_{red}$. We work with
two groups. The first one is a comparison between PISO, NFW, Spano and Burkert
showing that Spano is the most favored model satisfying our selection criteria.
For the second group we select soliton, NFW and Fuzzy models, resulting the
soliton as the best model. Moreover according to the statistical tools and
non-parametric reconstruction we are able to classify galaxies as core or cusp.
Finally, using an MCMC method, we compute for each of the DM models the
characteristic surface density, $\mu_{DM}=\rho_s r_s$, and the mass within 300
pc. We found that there is a common mass for spiral galaxies of the order of
$10^7$ M$_\odot$, which is in agreement with results for dSph Milky Way
satellites, independent of the model. This result is also consistent with our
finding that there is a constant characteristic volume density of haloes.
Finally, we also find that $\mu_{DM}$ is not constant, which is in tension with
previous literature.
