An approximate necessary condition for the optimal bandwidth selector in kernel density estimation

L. Gajek; A. Lenic

Applicationes Mathematicae (1993)

  • Volume: 22, Issue: 1, page 123-138
  • ISSN: 1233-7234

Abstract

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An approximate necessary condition for the optimal bandwidth choice is derived. This condition is used to construct an iterative bandwidth selector. The algorithm is based on resampling and step-wise fitting the bandwidth to the density estimator from the previous iteration. Examples show fast convergence of the algorithm to the bandwidth value which is surprisingly close to the optimal one no matter what is the initial knowledge on the unknown density.

How to cite

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Gajek, L., and Lenic, A.. "An approximate necessary condition for the optimal bandwidth selector in kernel density estimation." Applicationes Mathematicae 22.1 (1993): 123-138. <http://eudml.org/doc/219077>.

@article{Gajek1993,
abstract = {An approximate necessary condition for the optimal bandwidth choice is derived. This condition is used to construct an iterative bandwidth selector. The algorithm is based on resampling and step-wise fitting the bandwidth to the density estimator from the previous iteration. Examples show fast convergence of the algorithm to the bandwidth value which is surprisingly close to the optimal one no matter what is the initial knowledge on the unknown density.},
author = {Gajek, L., Lenic, A.},
journal = {Applicationes Mathematicae},
keywords = {bandwidth selection; kernel density estimation; resampling; self-learning algorithm; approximate necessary condition; optimal bandwidth choice; iterative bandwidth selector; stepwise fitting; fast convergence},
language = {eng},
number = {1},
pages = {123-138},
title = {An approximate necessary condition for the optimal bandwidth selector in kernel density estimation},
url = {http://eudml.org/doc/219077},
volume = {22},
year = {1993},
}

TY - JOUR
AU - Gajek, L.
AU - Lenic, A.
TI - An approximate necessary condition for the optimal bandwidth selector in kernel density estimation
JO - Applicationes Mathematicae
PY - 1993
VL - 22
IS - 1
SP - 123
EP - 138
AB - An approximate necessary condition for the optimal bandwidth choice is derived. This condition is used to construct an iterative bandwidth selector. The algorithm is based on resampling and step-wise fitting the bandwidth to the density estimator from the previous iteration. Examples show fast convergence of the algorithm to the bandwidth value which is surprisingly close to the optimal one no matter what is the initial knowledge on the unknown density.
LA - eng
KW - bandwidth selection; kernel density estimation; resampling; self-learning algorithm; approximate necessary condition; optimal bandwidth choice; iterative bandwidth selector; stepwise fitting; fast convergence
UR - http://eudml.org/doc/219077
ER -

References

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  1. J. J. Faraway and M. Jhun (1990), Bootstrap choice of bandwidth for density estimation, J. Amer. Statist. Assoc. 85, 1119-1122 
  2. W. Härdle, P. Hall and J. S. Marron (1988), How far are automatically chosen regression smoothing parameters from their optimum? (with comments), ibid. 74, 105-131 Zbl0644.62048
  3. C. Léger, D. N. Politis and J. P. Romano (1992), Bootstrap technology and applications, Technometrics 43, 378-398 Zbl0850.62367
  4. E. Parzen (1962), On estimation of a probability density function and mode, Ann. Math. Statist. 33, 1065-1076 Zbl0116.11302
  5. M. Rosenblatt (1956), Remarks on some nonparametric estimates of a density function, ibid. 27, 832-837 Zbl0073.14602
  6. B. W. Silverman (1986), Density Estimation for Statistics and Data Analysis, Chapman and Hall, London Zbl0617.62042
  7. C. C. Taylor (1989), Bootstrap choice of the smoothing parameter in kernel density estimation, Biometrika 76, 705-712. Zbl0678.62042

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