Asymptotically minimax nonparametric estimation of a regression function observed in white Gaussian noise over a bounded interval is considered, with respect to a L<sub>2</sub>-loss function. The unknown function f is assumed to be m times differentiable except for an unknown although finite number of jumps, with piecewise mth derivative bounded in L<sub>2</sub> norm. An estimator is constructed, attaining the same optimal risk bound, known as Pinsker's constant, as in the case of smooth functions (without jumps).
|Number of pages||19|
|Publication status||Published - Mar 1998|
- jump-point estimation
- nonparametric regression
- optimal constant
- tapered orthogonal series estimator