  We introduce a novel methodology for establishing the presence of Standing
Accretion Shock Instabilities (SASI) in the dynamics of a core collapse
supernova from the observed neutrino event rate at water- or ice-based neutrino
detectors. The methodology uses a likelihood ratio in the frequency domain as a
test-statistics; it is also employed to assess the potential to estimate the
frequency and the amplitude of the SASI modulations of the neutrino signal. The
parameter estimation errors are consistent with the minimum possible errors as
evaluated from the inverse of the Fisher information matrix, and close to the
theoretical minimum for the SASI amplitude. Using results from a core-collapse
simulation of a 15 solar-mass star by Kuroda $\it {et\, al.}$ (2017) as a test
bed for the method, we find that SASI can be identified with high confidence
for a distance to the supernova of up to $\sim 6$ kpc for IceCube and and up to
$\sim 3$ kpc for a 0.4 Mt mass water Cherenkov detector. This methodology will
aid the investigation of a future galactic supernova.
