| 摘要: |
| 大数据时代下收集到的数据常含有异常值或呈现尖峰厚尾以及变量之间具有较强的相关性，针对此问题，结合秩回归和自适应弹性网(Adaptive Elastic-net )提出了一种高效稳健的变量选择方法。此方法的最大优点在于不仅能够有效处理协变量之间的强相关性而且还能克服多重共线性问题，同时能抵抗厚尾分布或异常值的影响，实现稳健的变量选择。在数值计算方面，采用二次近似和牛顿迭代算法以获得新变量选择方法的稳定数值解，仿真实验表明：新提出的方法比现有方法表现更好，特别是对于厚尾分布或异常值的情况。最后，通过对中国重要的股票市场指数——中证100指数的跟踪，进一步表明该方法在有效样本下具有良好的表现。 |
| 关键词: 秩回归 弹性网约束 稳健估计 变量选择 中证100指 |
| DOI： |
| 分类号: |
| 基金项目: |
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| Robust Variable Selection Based on Elastic Network Constraint |
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WEI Shuang-wei
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(School of Mathematical Science, Chongqing Normal University, Chongqing 401331, China
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| Abstract: |
| In the era of big data, the collected data often contain outliers or present peak and thick tails and strong correlations between variables. To solve this problem, an efficient and robust variable selection method combining rank regression and Adaptive Elastic Net is proposed. The greatest advantage of this method is that it can not only effectively deal with the strong correlation among concomitant variables but also overcome the multicollinearity problem,and it can resist the influence of thick tailed distribution or outliers to achieve robust variable selection. In the aspect of numerical calculation, quadratic approximation and Newton iterative algorithm are used to obtain stable numerical solutions of the new variable selection method. Simulation results show that the proposed method performs better than the existing methods, especially for thick tailed distributions or outliers. Finally, through the tracking of CSI 100, an important stock market index in China, it is further demonstrated that this method has a good performance under effective samples. |
| Key words: rank regression elastic net constraint robust estimation variable selection CSI 100 |
