Inference for linear models with dependent errors
Inference for linear models with dependent errors
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DOI：
10.1111/j.1467-9868.2012.01044.x
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发表时间：
2013-01-01
影响因子：
5.8
通讯作者：
Shao, Xiaofeng
中科院分区：
文献类型：
--
作者：
Zhou, Zhou;Shao, Xiaofeng
.本文研究了具有固定回归变量和弱相依平稳时间序列误差的线性模型的推断问题。在理论上，我们在较弱的条件下得到了回归参数的M-估计的渐近正态性，并建立了递归M-估计的一致Bahadur表示。在方法上，我们最近提出的自规范化的方法邵从平稳的时间序列的回归设置，响应变量的序列通常是非平稳的平均值。由于自归一化统计量的极限分布依赖于设计矩阵，其相应的临界值是依赖于情况，我们开发了一种基于模拟的方法来近似的临界值一致。通过仿真研究，我们证明了有利的有限样本性能，我们的方法相比，基于块引导的方法。还提供了使用两个真实的数据集的经验说明。
. The paper is concerned with inference for linear models with fixed regressors and weakly dependent stationary time series errors. Theoretically, we obtain asymptotic normality for the M-estimator of the regression parameter under mild conditions and establish a uniform Bahadur representation for recursive M-estimators. Methodologically, we extend the recently proposed self-normalized approach of Shao from stationary time series to the regression set-up, where the sequence of response variables is typically non-stationary in mean. Since the limiting distribution of the self-normalized statistic depends on the design matrix and its corresponding critical values are case dependent, we develop a simulation-based approach to approximate the critical values consistently. Through a simulation study, we demonstrate favourable finite sample performance of our method in comparison with a block-bootstrap-based approach. Empirical illustrations using two real data sets are also provided.