We investigate the moment estimation for an ergodic diffusion process with unknown trend coefficient. We consider nonparametric and parametric estimation. In each case, we present a lower bound for the risk and then construct an asymptotically efficient estimator of the moment type functional or of a parameter which has a one-to-one correspondence to such a functional. Next, we clarify a higher order property of the moment type estimator by the Edgeworth expansion of the distribution function.
Publié le : 2007-11-14
Classification:
asymptotic efficiency,
asymptotic expansions,
diffusion process,
moment estimation,
nonparametric estimation
@article{1194625596,
author = {Kutoyants, Yury A. and Yoshida, Nakahiro},
title = {Moment estimation for ergodic diffusion processes},
journal = {Bernoulli},
volume = {13},
number = {1},
year = {2007},
pages = { 933-951},
language = {en},
url = {http://dml.mathdoc.fr/item/1194625596}
}
Kutoyants, Yury A.; Yoshida, Nakahiro. Moment estimation for ergodic diffusion processes. Bernoulli, Tome 13 (2007) no. 1, pp. 933-951. http://gdmltest.u-ga.fr/item/1194625596/