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Nonparametric regression with infinite order flat-top kernels

The problem of nonparametric regression is addressed, and a kernel smoothing estimator is proposed which has favorable asymptotic performance (bias, variance and mean squared error). The proposed class of kernels is characterized by a Fourier transform which is flat near the origin and infinitely differentiable. This property allows the bias of the estimate to decrease at the maximal rate without harming the rate at which the variance decreases, thus leading to a faster rate of convergence.