  We consider the problem of estimating a smooth functional of an unknown
signal with discontinuity from Gaussian observations. The signal is a known
function that depends on an unknown parameter. This problem is closely related
to the famous change-point problem. We obtain an asymptotic likelihood ratio
process for the noise level tending to 0. Bayesian and maximum likelihood
estimates are constructed and their relative efficiency is studied. Some
simulation results and conclusions on non-asymptotic behavior of these
estimates are presented.
