Performance of Non-Parametric Reconstruction Techniques in the Late-Time Universe

In the context of a Hubble tension problem that is growing in its statistical significance, we reconsider the effectiveness of non-parametric reconstruction techniques which are independent of prescriptive cosmological models. By taking cosmic chronometers, Type Ia Supernovae and baryonic acoustic oscillation data, we compare and contrast two important reconstruction approaches, namely Gaussian processes (GP) and the \textbf{Lo}cally w\textbf{e}ighted \textbf{S}catterplot \textbf{S}moothing together with \textbf{Sim}ulation and \textbf{ex}trapolation method (LOESS-Simex or LS). In the context of these methods, besides not requiring a cosmological model, they also do not require physical parameters in their approach to their reconstruction of data (but they do depend on statistical hyperparameters). We firstly show how both GP and LOESS-Simex can be used to successively reconstruct various data sets to a high level of precision. We then directly compare both approaches in a quantitative manner by considering several factors, such as how well the reconstructions approximate the data sets themselves to how their respective uncertainties evolve. In light of the puzzling Hubble tension, it is important to consider how the uncertain regions evolve over redshift and the methods compare for estimating cosmological parameters at current times. For cosmic chronometers and baryonic acoustic oscillation compiled data sets, we find that GP generically produce smaller variances for the reconstructed data with a minimum value of $\sigma_{\rm GP-min} = 1.1$, while the situation for LS is totally different with a minimum of $\sigma_{\rm LS-min} = 50.8$. Moreover, some of these characteristics can be alleviate at low $z$, where LS presents less underestimation in comparison to GP.