In this talk, we study properties of a new estimator for a fault line. This estimator is constructed by maximising a likelihood in a locally-linear model for the edge. The approach offers a unifying thread to spatial problems which are usually considered separately from each other. The convergence rate of the estimator comes within the known minimax-optimal convergence rate by an arbitrarily small power of the design intensity. Our main focus is on investigation of the local behaviour of this estimator, through which we obtain asymptotic confidence bands for the fault line, both pointwise and simultaneous.
Some artificial examples illustrate the feasibility and limitations of the results presented.