  In a recent study, the finite-time ($t$) and -population size ($N_c$)
scalings in the evaluation of a large deviation function (LDF) estimator were
analyzed by means of the cloning algorithm. These scalings provide valuable
information about the convergence of the LDF estimator in the infinite-$t$ and
infinite-$N_c$ limits. For the cases analyzed in that study, the scalings of
the systematic errors of the estimator were found to behave as $t^{-1}$ and
$N_c^{-1}$ in the large-$t$ and large-$N_c$ asymptotics. Moreover, it was shown
how this convergence speed can be used in order to extract an asymptotic limit
which resulted to render a better LDF estimation in comparison to the standard
estimator. However, the validity of these scaling laws and thus, the
convergence of the estimator was proved only in systems for which the number of
sites $L$ (where the dynamics occurs) was small. In this paper, the analysis is
extended to a wider range of system sizes $L$. We show how the introduction of
the exponents $\gamma_{t}$ and $\gamma_{N_c}$ allows to characterize the
behavior of the LDF estimator for any system size. From these generalized
$t^{-\gamma_{t}}$- and $N_{c}^{-\gamma_{N_c}}$- scalings, we verify that in the
large-$L$ limit the $t^{-1}$- and $N_c^{-1}$-scalings are no longer valid.
Moreover, as the convergence of the estimator relies on the positivity of these
exponents, we show how for some cases $\gamma_{N_c}$ can be negative implying
that the estimation provided by the cloning algorithm is no longer reliable.
