  We estimate constraints on the existence of a heavy, mostly sterile neutrino
with mass between 10 eV and 1 TeV. We improve upon previous analyses by
performing a global combination and expanding the experimental inputs to
simultaneously include tests for lepton universality, lepton-flavor-violating
processes, electroweak precision data, dipole moments, and neutrinoless double
beta decay. Assuming the heavy neutrino and its decay products are invisible to
detection, we further include, in a self-consistent manner, constraints from
direct kinematic searches, the kinematics of muon decay, cosmology, and
neutrino oscillations, in order to estimate constraints on the values of
$|U_{e4}|^2$, $|U_{\mu4}|^2$, and $|U_{\tau4}|^2$.
