Corpus ID: 57373890

Kernel Density Estimation Bias under Minimal Assumptions

@article{Skorski2019KernelDE,
  title={Kernel Density Estimation Bias under Minimal Assumptions},
  author={Maciej Skorski},
  journal={ArXiv},
  year={2019},
  volume={abs/1901.00331}
}
  • 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

References

SHOWING 1-10 OF 11 REFERENCES
Uniform Convergence Rates for Kernel Density Estimation
TLDR
Finite-sample high-probability density estimation bounds for multivariate KDE are derived under mild density assumptions which hold uniformly in x ∈ R and bandwidth matrices and uniform convergence results for local intrinsic dimension estimation are given. Expand
A Review of Kernel Density Estimation with Applications to Econometrics
TLDR
This comprehensive review summarizes the most important theoretical aspects of kernel density estimation and provides an extensive description of classical and modern data analytic methods to compute the smoothing parameter. Expand
Evaluation and Design of Filters Using a Taylor Series Expansion
TLDR
A new method for analyzing, classifying, and evaluating filters that can be applied to interpolation filters as well as to arbitrary derivative filters of any order, based on the Taylor series expansion of the convolution sum is described. Expand
Remarks on Some Nonparametric Estimates of a Density Function
1. Summary. This note discusses some aspects of the estimation of the density function of a univariate probability distribution. All estimates of the density function satisfying relatively mildExpand
On Estimation of a Probability Density Function and Mode
Abstract : Given a sequence of independent identically distributed random variables with a common probability density function, the problem of the estimation of a probability density function and ofExpand
Hadamard's Determinant Inequality
  • K. Lange
  • Mathematics, Computer Science
  • Am. Math. Mon.
  • 2014
TLDR
This note is devoted to a short, but elementary, proof of Hadamard's determinant inequality. Expand
Introduction to nonparametric statistics - lecture notes, http://faculty.washington.edu/yenchic/18W_425/Lec6_hist_KDE.pdf, 2018
  • 2018
Higher derivatives and taylors formula via multilinear maps, http://math.stanford.edu/~conrad/diffgeomPage/handouts/taylor.pdf
  • 2006
DUO 05 . Convergence rates for unconstrained bandwidth matrix selectors in multivariate kernel density estimation
  • Journal of Multivariate Analysis IEEE Transactions on Visualization and Computer Graphics
...
1
2
...