Change point estimation in noisy Hammerstein integral equations

TL;DRAbstract

We consider the inverse regression model Y = Hf (X) + ε for several classes of non- linear Hammerstein integral operators H. In particular identifiability depending on the integral kernel is discussed. We introduce estimators for parametric functions f with discontinuities of certain order including piecewise polynomials with kinks or jumps or free-knot splines respectively. We derive rates of convergence and asymptotic normality of these estimators and a data example from rheology illustrates the results. An ex- tension of the model for functions f from approximation spaces of parametric piecewise continuous functions is presented.

Chat with Paper

AI Agents for this Paper