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Annals of Statistics
We consider nonparametric estimation of an object such as a probability density or a regression function. Can such an estimator achieve the minimax rate of convergence on suitable function spaces, while, at the same time, when "plugged-in", estimate efficiently (at a rate of n −1/2 with the best constant) many functionals of the object? For example, can we have a density estimator whose definite integrals are efficient estimators of the cumulative distribution function? We show that this isdoi:10.1214/aos/1059655904 fatcat:iewyg4e4unad7divhxxrlo4mwe