A Convergence Result for a Class of Asymptotically Linear Estimators

作者：Atlagh M; Broniatowski M; Celant G^*

来源：Communications in Statistics - Theory and Methods, 2012, 41(16-17): 2922-2931.

DOI：10.1080/03610926.2011.593286

• Adaptive estimation
• Functional Glivenko-Cantelli theorem
• Last exit timer
• Strongly consistent estimation

This article provides the distribution of the last exit for strongly consistent estimators. Namely, we consider a small neighborhood of the (almost sure) limit and state the asymptotic distribution of the last time the estimator is outside this neighborhood. Such problems have been considered in the literature by various authors; this article extends these results in a semi-parametric frame. An application to adaptive estimation is provided.

• 出版日期2012