Asymptotically minimax estimation of a function with jumps
Oudshoorn, Catharina G.M.
Bernoulli, Tome 4 (1998) no. 1, p. 15-33 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
Asymptotically minimax nonparametric estimation of a regression function observed in white Gaussian noise over a bounded interval is considered, with respect to a L2-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 L2 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).
Publié le : 1998-03-14
Classification:  jump-point estimation,  nonparametric regression,  optimal constant,  tapered orthogonal series estimator 
@article{1175865488,
     author = {Oudshoorn, Catharina G.M.},
     title = {Asymptotically minimax estimation of a function with jumps},
     journal = {Bernoulli},
     volume = {4},
     number = {1},
     year = {1998},
     pages = { 15-33},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1175865488}
}

Oudshoorn, Catharina G.M. Asymptotically minimax estimation of a function with jumps. Bernoulli, Tome 4 (1998) no. 1, pp.  15-33. http://gdmltest.u-ga.fr/item/1175865488/