Bias correction and higher order kernel functions

Jianqing Fan, Tien Chung Hu

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


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)=∑k-11=0(kl+1)xlK(l)(x)/l! and [1/∫-∞K(k - 1)(x)/x d x]K(k - 1)(x)/x are kernels of order k, under some mild conditions.

Original languageEnglish (US)
Pages (from-to)235-243
Number of pages9
JournalStatistics and Probability Letters
Issue number3
StatePublished - Feb 19 1992
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


  • Bias correction
  • higher order kernel
  • kernel density estimate
  • nonparametrics


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