Wang Kai, Zhu Yanling
School of Statistics and Applied Mathematics, Anhui University of Finance and Economics, Bengbu, P.R. China.
J Inequal Appl. 2018;2018(1):225. doi: 10.1186/s13660-018-1819-3. Epub 2018 Aug 30.
We mainly study the M-estimation method for the high-dimensional linear regression model and discuss the properties of the M-estimator when the penalty term is a local linear approximation. In fact, the M-estimation method is a framework which covers the methods of the least absolute deviation, the quantile regression, the least squares regression and the Huber regression. We show that the proposed estimator possesses the good properties by applying certain assumptions. In the part of the numerical simulation, we select the appropriate algorithm to show the good robustness of this method.
我们主要研究高维线性回归模型的M估计方法，并讨论当惩罚项为局部线性近似时M估计量的性质。事实上，M估计方法是一个框架，它涵盖了最小绝对偏差法、分位数回归法、最小二乘回归法和Huber回归法。通过应用某些假设，我们证明了所提出的估计量具有良好的性质。在数值模拟部分，我们选择合适的算法来展示该方法良好的稳健性。
