Convolution of Kernels and Recursive Bias Correction

This paper exploits the convolution structure of the kernel estimator and proposes a recursive procedure to correct the bias. The procedure is equivalent to replacing the original kernel with a sequence of kernels constructed by convoluting the original one in a specific way. In the nonparametric setting, we show that one can further reduce the bias by making the order of such kernel exceeding rather than being equal to the order of differentiability of the function to be estimated. Furthermore, the semiparametric estimator based on such kernels enjoys the small bias property (SBP). Hence, the semiparametric estimator using this kernel has a smaller smoothing bias and a less restrictive condition on the bandwidth to achieve the asymptotic normality, compared to ordinary higher order kernels and the twicing kernel. The simulation study shows that the finite sample performance is consistent with the theoretical properties