A data-driven method of choosing the bandwidth, $h$, of a kernel density estimator is heuristically motivated by considering modifications of the Kullback-Leibler or pseudo-likelihood cross-validation function. It is seen that this means of choosing $h$ is asymptotically equivalent to taking the $h$ that minimizes some compelling error criteria such as the average squared error and the integrated squared error. Thus, for a given kernel function, the bandwidth can be chosen optimally without making precise smoothness assumptions on the underlying density.
Publié le : 1985-09-14
Classification:
Nonparametric density estimation,
kernel estimator,
bandwidth,
smoothing parameter,
cross-validation,
62G05,
62G20
@article{1176349653,
author = {Marron, James Stephen},
title = {An Asymptotically Efficient Solution to the Bandwidth Problem of Kernel Density Estimation},
journal = {Ann. Statist.},
volume = {13},
number = {1},
year = {1985},
pages = { 1011-1023},
language = {en},
url = {http://dml.mathdoc.fr/item/1176349653}
}
Marron, James Stephen. An Asymptotically Efficient Solution to the Bandwidth Problem of Kernel Density Estimation. Ann. Statist., Tome 13 (1985) no. 1, pp. 1011-1023. http://gdmltest.u-ga.fr/item/1176349653/