Based on empirical Lévy-type concentration functions, a new
graphical representation of the ML-density estimator under order restrictions
is given. This representation generalizes the well-known representation of the
Grenander estimator of a monotone density as the slope of the least concave
majorant of the empirical distribution function to higher dimensions and
arbitrary order restrictions. From the given representation it follows that a
density estimator called silhouette, which arises naturally out of the excess
mass approach, is the ML-density estimator under order restrictions. This fact
provides a new point of view to ML-density estimation from which one gains
additional insight to this problem, as demonstrated in the present paper.
Publié le : 1998-10-14
Classification:
Empirical processes,
excess mass,
Grenander density estimator,
level set estimation,
least concave majorant,
minimum volume sets,
nonparametric maximum likelihood estimation,
62G07,
62A10,
62G30,
62G20
@article{1024691360,
author = {Polonik, Wolfgang},
title = {The silhouette, concentration functions and ML-density estimation
under order restrictions},
journal = {Ann. Statist.},
volume = {26},
number = {3},
year = {1998},
pages = { 1857-1877},
language = {en},
url = {http://dml.mathdoc.fr/item/1024691360}
}
Polonik, Wolfgang. The silhouette, concentration functions and ML-density estimation
under order restrictions. Ann. Statist., Tome 26 (1998) no. 3, pp. 1857-1877. http://gdmltest.u-ga.fr/item/1024691360/