当前位置: X-MOL 学术Scand. J. Stat. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Preliminary test estimation in uniformly locally asymptotically normal models
Scandinavian Journal of Statistics ( IF 1 ) Pub Date : 2021-02-05 , DOI: 10.1111/sjos.12516
Davy Paindaveine 1, 2 , Joséa Rasoafaraniaina 1 , Thomas Verdebout 1
Affiliation  

Preliminary test estimation is a methodology that combines goodness-of-fit testing and estimation. It is a classical procedure when it is suspected that the parameter to be estimated satisfies some prespecified constraints. In the present paper, we establish general results on the asymptotic behavior of preliminary test estimators. More precisely, we show that, in uniformly locally asymptotically normal (ULAN) models, a general asymptotic theory can be derived for preliminary test estimators based on estimators admitting generic Bahadur-type representations. This allows for a detailed comparison between classical estimators and preliminary test estimators in ULAN models. Our results, that, in standard linear regression models, are shown to reduce to some classical results, are also illustrated in more modern and involved setups, such as the multisample one where m covariance matrices 1 , , m are to be estimated when it is suspected that these matrices might be equal, might be proportional, or might share a common “scale”. Simulation results confirm our theoretical findings and an illustration on a real data example is provided.

中文翻译:

均匀局部渐近正态模型中的初步测试估计

初步测试估计是一种结合了拟合优度测试和估计的方法。当怀疑要估计的参数满足一些预先指定的约束时,这是一个经典的过程。在本文中,我们建立了初步测试估计量渐近行为的一般结果。更准确地说,我们表明,在一致局部渐近正态 (ULAN) 模型中,可以基于接受通用 Bahadur 类型表示的估计器为初步测试估计器推导出一般渐近理论。这允许在 ULAN 模型中对经典估计量和初步测试估计量进行详细比较。我们的结果,在标准线性回归模型中,被证明可以简化为一些经典结果,也在更现代和更复杂的设置中得到说明,m协方差矩阵 1 , , 当怀疑这些矩阵可能相等、可能成比例或可能共享一个共同的“尺度”时,将被估计。仿真结果证实了我们的理论发现,并提供了真实数据示例的说明。
更新日期:2021-02-05
down
wechat
bug