  The 3X3 Maki-Nakagawa-Sakata-Pontecorvo (MNSP) lepton flavor mixing matrix
may be slightly non-unitary if the three active neutrinos are coupled with
sterile neutrinos. We show that it is in principle possible to test whether the
relation |V_{e1}|^2 + |V_{e2}|^2 + |V_{e3}|^2 = 1 holds or not in a precision
reactor antineutrino oscillation experiment, such as the recently proposed Daya
Bay II experiment. We explore three categories of non-unitary effects on the
3X3 MNSP matrix: 1) the indirect effect in the (3+ 3) flavor mixing scenario
where the three heavy sterile neutrinos do not take part in neutrino
oscillations; 2) the direct effect in the (3+\mathbbm{1}) scenario where the
light sterile neutrino can oscillate into the active ones; and 3) the interplay
of both of them in the (3+\mathbbm{1}+ 2) scenario. We find that both the
zero-distance effect and flavor mixing factors of different oscillation modes
can be used to determine or constrain the sum of |V_{e1}|^2, |V_{e2}|^2 and
|V_{e3}|^2 and its possible deviation from one, and the active neutrino mixing
angles \theta_{12} and \theta_{13} can be cleanly extracted even in the
presence of light or heavy sterile neutrinos. Some useful analytical results
are obtained for each of the three scenarios.
