  Statistical errors in ground state observables and single-particle properties
of spherical even-even nuclei and their propagation to the limits of nuclear
landscape have been investigated in covariant density functional theory (CDFT)
for the first time. In this study we consider only covariant energy density
functionals with non-linear density dependency. Statistical errors for binding
energies and neutron skins significantly increase on approaching two-neutron
drip line. On the contrary, such a trend does not exist for statistical errors
in charge radii and two-neutron separation energies. The absolute and relative
energies of the single-particle states in the vicinity of the Fermi level are
characterized by low statistical errors ($\sigma(e_i)\sim 0.1$ MeV).
Statistical errors in the predictions of spin-orbit splittings are rather
small. Statistical errors in physical observables are substantially smaller
than related systematic uncertainties. Thus, at the present level of the
development of theory, theoretical uncertainties at nuclear limits are
dominated by systematic ones. Statistical errors in the description of physical
observables related to the ground state and single-particle degrees of freedom
are typically substantially lower in CDFT as compared with Skyrme density
functional theory. The correlations between the model parameters are studied in
detail. The parametric correlations are especially pronounced for the $g_2$ and
$g_3$ parameters which are responsible for the density dependence of the model.
The accounting of this fact potentially allows to reduce the number of free
parameters of non-linear meson coupling model from six to five.
