In this paper we prove the Local Asymptotic Mixed Normality (LAMN) property for the statistical model given by the observation of local means of a diffusion process X. Our data are given by ∫01X(s+i)/n dμ(s) for i=0, …, n−1 and the unknown parameter appears in the diffusion coefficient of the process X only. Although the data are neither Markovian nor Gaussian we can write down, with help of Malliavin calculus, an explicit expression for the log-likelihood of the model, and then study the asymptotic expansion. We actually find that the asymptotic information of this model is the same one as for a usual discrete sampling of X.
@article{1203969870,
author = {Gloter, Arnaud and Gobet, Emmanuel},
title = {LAMN property for hidden processes: The case of integrated diffusions},
journal = {Ann. Inst. H. Poincar\'e Probab. Statist.},
volume = {44},
number = {2},
year = {2008},
pages = { 104-128},
language = {en},
url = {http://dml.mathdoc.fr/item/1203969870}
}
Gloter, Arnaud; Gobet, Emmanuel. LAMN property for hidden processes: The case of integrated diffusions. Ann. Inst. H. Poincaré Probab. Statist., Tome 44 (2008) no. 2, pp. 104-128. http://gdmltest.u-ga.fr/item/1203969870/