论文标题
包裹的Huber回归
Enveloped Huber Regression
论文作者
论文摘要
当误差遵循重型分布时，Huber回归（HR）是最小二乘回归的一种流行稳健替代方案。我们提出了一种新方法，称为包络的Huber回归（EHR），它考虑了一个包络假设，即存在与响应没有关联的预测因子的某个子空间，这被称为非物质部分。通过去除非物质部分来实现更有效的估计。与估计基于最大正常可能性的估计的包络最小二乘模型不同，EHR模型的估计是通过一般矩的通用方法。建立了EHR估计量的渐近正态性，这表明EHR比HR更有效。此外，当误差分布被重尾时，EHR比ENV更有效，同时在误差分布正常时保持效率较小。此外，我们的理论还涵盖了误差可能取决于协变量的异质案例。广泛的仿真研究证实了渐近理论的信息。在真实数据集中进一步说明了EHR。
Huber regression (HR) is a popular robust alternative to the least squares regression when the error follows a heavy-tailed distribution. We propose a new method called the enveloped Huber regression (EHR) by considering the envelope assumption that there exists some subspace of the predictors that has no association with the response, which is referred to as the immaterial part. More efficient estimation is achieved via the removal of the immaterial part. Different from the envelope least squares (ENV) model whose estimation is based on maximum normal likelihood, the estimation of the EHR model is through Generalized Method of Moments. The asymptotic normality of the EHR estimator is established, and it is shown that EHR is more efficient than HR. Moreover, EHR is more efficient than ENV when the error distribution is heavy-tailed, while maintaining a small efficiency loss when the error distribution is normal. Moreover, our theory also covers the heteroscedastic case in which the error may depend on the covariates. Extensive simulation studies confirm the messages from the asymptotic theory. EHR is further illustrated on a real dataset.
