We consider the problem of $L_p$-consistent density estimation from
the initial segments of strongly dependent processes. It is shown that no
procedure can consistently estimate the one-dimensional marginal density of
every stationary ergodic process for which such a density exists. A similar
result is established for the problem of estimating the support of the marginal
distribution of an ergodic process.
Publié le : 1998-04-14
Classification:
Density estimation,
ergodic processes,
cutting and stacking,
counter-example,
62G07,
60G17,
60G10
@article{1022855650,
author = {Adams, Terrence M. and Nobel, Andrew B.},
title = {On density estimation from ergodic processes},
journal = {Ann. Probab.},
volume = {26},
number = {1},
year = {1998},
pages = { 794-804},
language = {en},
url = {http://dml.mathdoc.fr/item/1022855650}
}
Adams, Terrence M.; Nobel, Andrew B. On density estimation from ergodic processes. Ann. Probab., Tome 26 (1998) no. 1, pp. 794-804. http://gdmltest.u-ga.fr/item/1022855650/