- Volume 4, Number 1 (1998), 15-33.
Asymptotically minimax estimation of a function with jumps
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).
Bernoulli, Volume 4, Number 1 (1998), 15-33.
First available in Project Euclid: 6 April 2007
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Oudshoorn, Catharina G.M. Asymptotically minimax estimation of a function with jumps. Bernoulli 4 (1998), no. 1, 15--33. https://projecteuclid.org/euclid.bj/1175865488