  In sterile neutrino scenarios, radiative corrections induce mass splittings
proportional to the top Yukawa coupling, in contrast to the three active
neutrino case where the induced splittings are proportional to the tau Yukawa
coupling. In view of this, we have analyzed the stability of the four-neutrino
schemes favored by oscillation experiments, consisting in two pairs of nearly
degenerate neutrinos separated by the LSND gap. Requiring compatibility with
the measurements of the abundances of primordial elements produced in Big Bang
Nucleosynthesis, we find that when the heaviest pair corresponds to the solar
neutrinos (mainly an admixture of nu_e - nu_s) the natural mass splitting is
3-5 orders of magnitude larger than the observed one, discrediting the scenario
from a theoretical point of view. On the contrary, the scheme where the
heaviest pair corresponds to the atmospheric neutrinos (mainly an admixture of
nu_mu - nu_tau) is safe from radiative corrections due to the small sterile
component of these mass eigenstates.
