We investigate the behavior of the nonparametric maximum likelihood estimator f̂n for a decreasing density f near the boundaries of the support of f. We establish the limiting distribution of f̂n(n−α), where we need to distinguish between different values of 0<α<1. Similar results are obtained for the upper endpoint of the support, in the case it is finite. This yields consistent estimators for the values of f at the boundaries of the support. The limit distribution of these estimators is established and their performance is compared with the penalized maximum likelihood estimator.
Publié le : 2006-04-14
Classification:
Grenander estimator,
estimating a monotone density at zero,
isotonic estimation,
asymptotic distribution,
62G07,
62E20,
62G20
@article{1151418239,
author = {Kulikov, Vladimir N. and Lopuha\"a, Hendrik P.},
title = {The behavior of the NPMLE of a decreasing density near the boundaries of the support},
journal = {Ann. Statist.},
volume = {34},
number = {1},
year = {2006},
pages = { 742-768},
language = {en},
url = {http://dml.mathdoc.fr/item/1151418239}
}
Kulikov, Vladimir N.; Lopuhaä, Hendrik P. The behavior of the NPMLE of a decreasing density near the boundaries of the support. Ann. Statist., Tome 34 (2006) no. 1, pp. 742-768. http://gdmltest.u-ga.fr/item/1151418239/