This paper studies some asymptotic properties of density estimates $\hat{f}$ of $f$ based on $d$-variate delta sequences. The mean-square consistency, almost sure consistency, and asymptotic normality of $\hat{f}$ have been obtained as corollaries to the $L_1$ convergence properties of these delta sequences. Estimators based on kernel functions, orthogonal series, and some histogram methods can be obtained as special cases of $\hat{f}$.
Publié le : 1981-03-14
Classification:
Density estimation,
delta sequences,
mean square convergence,
asymptotic normality,
62F10,
62G05,
41A25,
46F99
@article{1176345400,
author = {Susarla, V. and Walter, G.},
title = {Estimation of a Multivariate Density Function Using Delta Sequences},
journal = {Ann. Statist.},
volume = {9},
number = {1},
year = {1981},
pages = { 347-355},
language = {en},
url = {http://dml.mathdoc.fr/item/1176345400}
}
Susarla, V.; Walter, G. Estimation of a Multivariate Density Function Using Delta Sequences. Ann. Statist., Tome 9 (1981) no. 1, pp. 347-355. http://gdmltest.u-ga.fr/item/1176345400/