Asymptotically Minimax Estimation of a Function with Jumps
نویسنده
چکیده
Asymptotically minimax nonparametric estimation of a regression function observed in white Gaussian noise over a bounded interval is considered, with respect to a L 2-loss function. The unknown function f is assumed to be m times diierentiable except for an unknown, though nite, number of jumps, with piecewise mth derivative bounded in L 2-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).
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