NDLI: Exact asymptotic bias for estimators of the Ornstein

Content Provider	Springer Nature Link
Author	Bosq, Denis
Copyright Year	2010
Abstract	We study the bias and the bias derivative for a family $${\mathcal{F}}$$ of asymptotically efficient estimators of the Ornstein–Uhlenbeck process. That family contains the maximum likelihood, the conditional maximum likelihood and the empirical estimators. We show that, if g(θ $_{T}$) is an estimator of g(θ), where θ is the parameter and $${\theta_{T} \in \mathcal{F}}$$ , then, under mild conditions, $$T\,E\left[g(\theta_{T})-g(\theta)\right]\xrightarrow[T\rightarrow\infty]{}c_{\theta}g^{\prime}(\theta)+\theta{g}^{\prime\prime}(\theta),$$ where c $_{θ}$ is an explicit constant that only depends on the choice of θ $_{T}$. In particular, if θ $_{T}$ is one of the three previous estimators, one has $$T\,E_{\theta}(\theta_{T}-\theta)\xrightarrow[T\rightarrow\infty]\,2.$$
Ending Page	145
Page Count	13
Starting Page	133
File Format	PDF
ISSN	13870874
e-ISSN	15729311
Journal	Statistical Inference for Stochastic Processes
Issue Number	2
Volume Number	13
Language	English
Publisher	Springer Netherlands
Publisher Date	2010-04-23
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Bias derivative Asymptotic bias Empirical estimator Inference from stochastic processes Asymptotic properties of estimators Point estimation Probability Theory and Stochastic Processes Ornstein–Uhlenbeck process Maximum likelihood Conditional maximum likelihood Asymptotic efficiency
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability

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