OPTIMAL GLOBAL RATES OF CONVERGENCE FOR NONPARAMETRIC ESTIMATORS

By C. Stone. 1982

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Citations in the corpus

Minimax estimation via wavelet shrinkage (1998, background): “Ž .well studied e.g., Ibragimov and Khas’minskii 1982 , Stone 1982 , NussŽ .”
Fast, smooth and adaptive regression in metric spaces (2009, background): “This so-called curse of dimensionality is quantified by various lower bounds on the convergence rates of the form n −2/(2+D) for data in R D (see e.g. [3] [4]).”
Adapting to Unknown Smoothness via Wavelet Shrinkage (1995, background): “By direct calculation, E jj~ jj(2)2 = jj jj(2)2=(jj jj(2)2 + d): (32) The di erence of (32) and (32) is thus bounded by (2d 4)=(jj jj2 2 + d) 2:”
Wavelet Shrinkage: Asymptopia? (1995, methodology): “Bretagnolle and Huber (1979), Stone (1982), and Ibragimov and Has'minskii (1982) studied problems of estimating the whole object with global loss kf̂n fkpLp and Lp Sobolev a-priori class W p m (C) (same p in both), and found that certain kernel estimates attain the minimax rate { i.e. achieve (11).”
Strong Universal Consistency of Neural Network Classifiers (1993, background): “Stone [25] showed for regression estimation that the optimal rate of convergence is of this type, that is, no estimator can yield faster rate of convergence.”
A moving window approach for nonparametric estimation of the conditional tail index (2008, methodology): “ = E(logY|X = x). Let us highlight that the convergence rate provided by Corollary 2 is, up to the ηn factor, the optimal convergence rate for estimating α-Lipschitzian regression function in Rp, see [30]. 7 4 Discussion on thechoiceof the weights In order to illustrate the usefulness of our results”