Change point estimation in noisy Hammerstein integral equations [thesis]

Frick Sophie
We consider the inverse regression model Y = Hf (X) + ε for several classes of nonlinear 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
more » ... results. An extension of the model for functions f from approximation spaces of parametric piecewise continuous functions is presented. 7 Approximation spaces 7.1 Definition .
doi:10.53846/goediss-2491 fatcat:dhi3t7s3yzapfozlbnzmp4ouwa