Asymptotic theory of semiparametric z-estimators for stochastic processes with applications to ergodic diffusions and time series

Yoichi Nishiyama*

*この研究の対応する著者

研究成果: Article査読

5 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)3555-3579
ページ数25
ジャーナルAnnals of Statistics
37
6 A
DOI
出版ステータスPublished - 2009 12月
外部発表はい

ASJC Scopus subject areas

  • 統計学および確率
  • 統計学、確率および不確実性

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