This paper generalizes a part of the theory of Z-estimation which has been developed mainly in the context of modern empirical processes to the case of stochastic processes, typically, semimartingales. We present a general theorem to derive the asymptotic behavior of the solution to an estimating equation θ↝Ψn(θ, ĥn)=0 with an abstract nuisance parameter h when the compensator of Ψn is random. As its application, we consider the estimation problem in an ergodic diffusion process model where the drift coefficient contains an unknown, finite-dimensional parameter θ and the diffusion coefficient is indexed by a nuisance parameter h from an infinite-dimensional space. An example for the nuisance parameter space is a class of smooth functions. We establish the asymptotic normality and efficiency of a Z-estimator for the drift coefficient. As another application, we present a similar result also in an ergodic time series model.
@article{1250515396,
author = {Nishiyama, Yoichi},
title = {Asymptotic theory of semiparametric Z-estimators for stochastic processes with applications to ergodic diffusions and time series},
journal = {Ann. Statist.},
volume = {37},
number = {1},
year = {2009},
pages = { 3555-3579},
language = {en},
url = {http://dml.mathdoc.fr/item/1250515396}
}
Nishiyama, Yoichi. Asymptotic theory of semiparametric Z-estimators for stochastic processes with applications to ergodic diffusions and time series. Ann. Statist., Tome 37 (2009) no. 1, pp. 3555-3579. http://gdmltest.u-ga.fr/item/1250515396/