We provide a general method to analyze the asymptotic properties of a variety of estimators of continuous time diffusion processes when the data are not only discretely sampled in time but the time separating successive observations may possibly be random. We introduce a new operator, the generalized infinitesimal generator, to obtain Taylor expansions of the asymptotic moments of the estimators. As a special case, our results apply to the situation where the data are discretely sampled at a fixed nonrandom time interval. We include as specific examples estimators based on maximum-likelihood and discrete approximations such as the Euler scheme.
Publié le : 2004-10-14
Classification:
Diffusions,
likelihood,
discrete and random sampling,
62F12,
62M05,
60H10,
60J60
@article{1098883787,
author = {A\"\i t-Sahalia, Yacine and Mykland, Per A.},
title = {Estimators of diffusions with randomly spaced discrete observations: A general theory},
journal = {Ann. Statist.},
volume = {32},
number = {1},
year = {2004},
pages = { 2186-2222},
language = {en},
url = {http://dml.mathdoc.fr/item/1098883787}
}
Aït-Sahalia, Yacine; Mykland, Per A. Estimators of diffusions with randomly spaced discrete observations: A general theory. Ann. Statist., Tome 32 (2004) no. 1, pp. 2186-2222. http://gdmltest.u-ga.fr/item/1098883787/