Bias correction and higher order kernel functions

Jianqing Fan and Tien-Chung Hu

Statistics & Probability Letters, 1992, vol. 13, issue 3, 235-243

Abstract: Kernel density estimates are frequently used, based on a second order kernel. Thus, the bias inherent to the estimates has an order of O(h2n). In this note, a method of correcting the bias in the kernel density estimates is provided, which reduces the bias to a smaller order. Effectively, this method produces a higher order kernel based on a second order kernel. For a kernel function K, the functions Wk(x)=[summation operator]k-11=0(kl+1)xlK(l)(x)/l! and [1/[integral operator][infinity]-[infinity]K(k - 1)(x)/x d x]K(k - 1)(x)/x are kernels of order k, under some mild conditions.

Keywords: Bias; correction; higher; order; kernel; kernel; density; estimate; nonparametrics (search for similar items in EconPapers)
Date: 1992
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Citations: View citations in EconPapers (3)

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