  We study nonparametric change-point estimation from indirect noisy
observations. Focusing on the white noise convolution model, we consider two
classes of functions that are smooth apart from the change-point. We establish
lower bounds on the minimax risk in estimating the change-point and develop
rate optimal estimation procedures. The results demonstrate that the best
achievable rates of convergence are determined both by smoothness of the
function away from the change-point and by the degree of ill-posedness of the
convolution operator. Optimality is obtained by introducing a new technique
that involves, as a key element, detection of zero crossings of an estimate of
the properly smoothed second derivative of the underlying function.
