基于弹性网惩罚的复合分位数回归估计

针对高维数据的建模分析问题,提出一种基于弹性网络法和复合分位数回归相结合的稳健估计方法。 在该 估计方法中,所提出的模型能够有效进行变量选择与系数压缩,并处理数据间的多重共线性与群组效应问题,在大 数据时代下具有较广的适应性。 同时,与已有的惩罚最小二乘估计和惩罚分位数回归估计相比,该估计方法不仅 放宽了对模型误差项的分布要求,而且综合考虑了多个分位点的损失,在面对离群值或呈现尖峰、厚尾分布数据时 能够保持更强的稳健性和抗干扰性。 在一定条件下,对所构建模型估计的相合性与稀疏性进行了理论分析,结果 表明:所提出的模型能够将不相关的变量完全压缩至零,且估计量和真实系数以趋于 1 的概率相同。 此外,在数值 模拟方面,设置了 5 种误差项分布条件,根据设定的 4 项指标,通过与其他惩罚函数模型以及损失函数模型进行比 较,结果表明新提出的方法具备更好的稳健性与有效性。

Compound Quantile Regression Model with Elastic Net Penalty

Aiming at the problem of modeling and analysis under high-dimensional data a robust estimation method based on elastic network method and composite quantile regression was proposed. In this estimation method the proposed model can effectively perform variable selection and coefficient compression and deal with multicollinearity and group effects between data and has wide adaptability in the era of big data. At the same time compared with the existing penalized least squares estimation and penalized quantile regression estimation this estimation method not only relaxes the distribution requirements of the model error term but also comprehensively considers the loss of multiple quantiles which can maintain stronger robustness and anti-interference in the face of outliers or data with spiky thick-tailed distributions. Under certain conditions a theoretical analysis of the consistency and sparsity of the constructed model estimates is carried out. The results show that the proposed model can completely compress uncorrelated variables to zero and the estimate and the true coefficient have the same probability of tending to 1. In addition in terms of numerical simulation five kinds of error term distribution conditions are set. According to the four indicators set the comparison with other penalty function models and loss function models is carried out. The results show that the newly proposed method has better robustness and effectiveness.