  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.
