Corpus ID: 57373890

Kernel Density Estimation Bias under Minimal Assumptions

  title={Kernel Density Estimation Bias under Minimal Assumptions},
  author={Maciej Skorski},
  • M. Skorski
  • Published 2 January 2019
  • Mathematics, Computer Science
  • ArXiv
Kernel Density Estimation is a very popular technique of approximating a density function from samples. The accuracy is generally well-understood and depends, roughly speaking, on the kernel decay and local smoothness of the true density. However concrete statements in the literature are often invoked in very specific settings (simplified or overly conservative assumptions) or miss important but subtle points (e.g. it is common to heuristically apply Taylor's expansion globally without… Expand


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  • K. Lange
  • Mathematics, Computer Science
  • Am. Math. Mon.
  • 2014
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Introduction to nonparametric statistics - lecture notes,, 2018
  • 2018
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  • 2006
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  • Journal of Multivariate Analysis IEEE Transactions on Visualization and Computer Graphics