中文摘要：

变量选择是统计建模的重要环节,选择合适的变量可以建立结构简单、预测精准的稳健模型.本文在logistic回归下提出了新的双层变量选择惩罚方法——adaptive Sparse Group Lasso（adSGL）,其独特之处在于基于变量的分组结构进行筛选,实现了组内和组间双层选择.该方法的优点是对各单个系数和组系数采取不同程度的惩罚,避免了过度惩罚大系数,从而提高了模型的估计和预测精度.求解的难点是惩罚似然函数不是严格凸出的,因此本文基于组坐标下降法求解模型,并建立了调整参数的选取准则.模拟分析表明,对比现有代表性方法Sparse Group Lasso、Group Lasso及Lasso,adSGL法不仅提高了双层选择精度,而且降低了模型误差.最后,本文将adSGL法应用于信用卡信用评分研究,与logistic回归相比,其具有更高的分类精度和稳健性.

英文摘要：

Variable selection is of great importance in statistical modeling. Suitable variables can make the model simple and have favorite performance of prediction. We propose a novel penalized bi-level variable selection method- adaptive Sparse Group Lasso （adSGL） , under the framework of logistic regression. Its uniqueness is that it does selection based on the grouping structure of predictors, which realizes selections at both group and individual level. It has the advantage of allowing different amounts of shrinkage for different individuals and groups, which can avoid over shrinkage for large coefficients and improve the accuracies of estimate and prediction. The difficulties of solution lies in the non-strict convexity of the penalized likelihood function so we solve the model based on block coordinate descent and establish selection criteria of tuning parameter. Simulation studies show that in compare with three representative methods Sparse Group Lasso,Group Lasso and Lasso, adSGL not only enhances bi-level selection accuracy, but also reduces model error. In the application of credit card credit scoring dataset shows that in compare with logistic regression, adSGL method has higher classification accuracy and better robustness.