OPTIMAL CHANGE-POINT ESTIMATION IN INVERSE PROBLEMS

We develop a method of estimating a change-point of an otherwise smoot h function in the case of indirect noisy observations. As two paradigm s we consider deconvolution and non-parametric errors-in-variables reg ression. In a similar manner to well-established methods for estimatin g change-points in non-parametric regression, we look essentially at t he difference of one-sided kernel estimators. Because of the indirect nature of the observations we employ deconvoluting kernels. We obtain an estimate of the change-point by the extremal point of the differenc es between these two-sided kernel estimators. We derive rates of conve rgence for this estimator. They depend on the degree of ill-posedness of the problem, which derives from the smoothness of the error density . Analysing the Hellinger modulus of continuity of the problem we show that these rates are minimax.