The asymptotics of MM-estimators for linear regression with fixed designs
The asymptotics of MM-estimators for linear regression with fixed designs
复制标题
DOI：
10.1007/s00184-005-0019-6
复制
发表时间：
2006-06-01
期刊：
影响因子：
0.7
通讯作者：
Salibian-Barrera, M
中科院分区：
文献类型：
--
作者：
Salibian-Barrera, M
MM-估计实现同时高效率和高崩溃点污染的社区。基于这些估计量的推断依赖于它们的渐近性质，这些性质已经在随机协变量的情况下进行了研究。本文证明了在相对较弱的正则性条件下，当设计固定时，线性回归模型的MM-估计是强相合的。此外，他们的强一致性使我们能够证明，这些估计也是渐近正常的非随机协变量。这些结果证明了使用一个正常的近似的有限样本分布的MM估计的线性回归固定的解释变量。此外，这些结果还被用于将稳健引导法（Salibian-Barrera and Zelvis in Ann Stat 30：556-582，2002）扩展到固定设计的情况[参见Salibian-Barrera 2004，已提交]。
MM-estimators achieve simultaneous high efficiency and high breakdown point over contamination neighborhoods. Inference based on these estimators relies on their asymptotic properties, which have been studied for the case of random covariates. In this paper we show that, under relatively mild regularity conditions, MM-estimators for linear regression models are strongly consistent when the design is fixed. Moreover, their strong consistency allows us to show that these estimators are also asymptotically normal for non-random covariates. These results justify the use of a normal approximation to the finite-sample distribution of MM-estimators for linear regression with fixed explanatory variables. Additionally, these results have been used to extend the robust bootstrap (Salibian-Barrera and Zamar in Ann Stat 30:556-582, 2002) to the case of fixed designs [see Salibian-Barrera 2004, submitted].