Optimal change-point estimation in inverse problems
- Neumann, Michael H.
2010 Mathematics Subject Classification
- 62G05 62G20
- Change-point estimation, inverse problems, indirect observations, deconvolution, errors-in-variables regression, optimal rates of convergence
We develop a method of estimating change-points of a function in the case of indirect noisy observations. As two paradigmatic problems we consider deconvolution and errors-in-variables regression. We estimate the scalar products of our indirectly observed function with appropriate test functions, which are shifted over the interval of interest. An estimator of the change point is obtained by the extremal point of this quantity. We derive rates of convergence for this estimator. They depend on the degree of ill-posedness of the problem, which derives from the smoothness of the error density. Analyzing the Hellinger modulus of continuity of the problem we show that these rates are minimax.