We study maximum penalized likelihood density estimation using the
first roughness penalty functional of Good. We prove a simple pointwise
comparison result with a kernel estimator based on the two-sided exponential
kernel. This leads to $L^1$ convergence results similar to those for kernel
estimators. We also prove Hellinger distance bounds for the roughness penalized
estimator.
Publié le : 1999-10-14
Classification:
Nonparametric density estimation,
maximum likelihood,
roughness penalization,
Hellinger distance,
62G07
@article{1017939143,
author = {Eggermont, P. P. B. and LaRiccia, V. N.},
title = {Optimal convergence rates for Good's nonparametric maximum
likelihood density estimator},
journal = {Ann. Statist.},
volume = {27},
number = {4},
year = {1999},
pages = { 1600-1615},
language = {en},
url = {http://dml.mathdoc.fr/item/1017939143}
}
Eggermont, P. P. B.; LaRiccia, V. N. Optimal convergence rates for Good's nonparametric maximum
likelihood density estimator. Ann. Statist., Tome 27 (1999) no. 4, pp. 1600-1615. http://gdmltest.u-ga.fr/item/1017939143/