We construct a data-driven projection density estimator for continuous time processes. This estimator reaches superoptimal rates over a class F0 of densities that is dense in the family of all possible densities, and a «reasonable» rate elsewhere. The class F0 may be chosen previously by the analyst. Results apply to Rd-valued processes and to N-valued processes. In the particular case where square-integrable local time does exist, it is shown that our estimator is strictly better than the local time estimator over F0.
@article{urn:eudml:doc:40450,
title = {Local superefficiency of data-driven projection density estimators in continuous time.},
journal = {SORT},
volume = {28},
year = {2004},
pages = {37-54},
mrnumber = {MR2076035},
zbl = {1274.62265},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:40450}
}
Bosq, Denis; Blanke, Delphine. Local superefficiency of data-driven projection density estimators in continuous time.. SORT, Tome 28 (2004) pp. 37-54. http://gdmltest.u-ga.fr/item/urn:eudml:doc:40450/