Logistic回归的ArctanLASSO惩罚似然估计及应用

Logistic回归是计量经济学中应用最广的离散选择模型。当变量个数较多时，极大似然估计解释性较差，为此本文基于新的惩罚函数ArctanLASSO，给出Logistic回归的一种非凸惩罚似然估计进行参数估计和变量选取，并证明了估计量的n1/2相合性和Oracle性质。本文结合二阶近似处理、LLA方法和梯度下降法给出估计算法，并通过最小化BIC准则对正则化参数进行选取。模拟数据分析显示，当样本量较大时，该方法在参数估计和变量选取两个方面都优于传统的LASSO、SCAD和MCP方法，样本量较小时，该方法同样具有很大优势。实际数据分析表明，该方法很好地权衡了拟合程度和非零系数的选择，是最优的备选模型，具有重要的实际意义。

ArctanLASSO Penalized Likelihood Estimator of Logistic Regression and Its Application

Logistic regression is a discrete choice model widely used in econometrics. A large number of predictors will make the model hard to interpret,so this paper proposes a new concave penalized estimator via ArctanLASSO to carry on parameter estimation and variable selection simultaneously. We prove that the proposed approach is root-n consistent and enjoys the Oracle property. An algorithm is presented by combining second-order Taylor expansion,LLA and coordinate descent algorithm,and tuning parameter is selected by BIC criterion. Simulation study shows that ArctanLASSO estimator is better than traditional methods in large sample and has comparable performance in small sample. Real data analysis suggests that ArctanLASSO estimator is a good candidate in terms of obtaining desired sparsity-fit trade-off.