ASYMPTOTIC THEORY OF SEMIPARAMETRIC Z-ESTIMATORS FOR STOCHASTIC PROCESSES WITH APPLICATIONS TO ERGODIC DIFFUSIONS AND TIME SERIES

• 成果类型: Article
• 署名作者: Nishiyama, Yoichi
• 署名单位: Research Organization of Information & Systems (ROIS); Institute of Statistical Mathematics (ISM) - Japan
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/09-AOS693
• 发表日期: 2009
• 页码: 3555-3579
• 关键词: WEAK-CONVERGENCE; martingales

摘要

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 theta (sic) Psi(n) (theta, (h) over cap (n)) = 0 with an abstract nuisance parameter h when the compensator of Psi(n) 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 theta 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.