关键词: 高维阈值模型, 稀疏特征, 变量选择, 参数估计, Karush-Kuhn-Tucker条件

Abstract: Threshold regression model is an important class of models that characterize nonlinear relationships in economics. However, the conventional threshold estimate is found to have nonstandard asymptotic distribution and conservative confidence regions, making it inconvenient to be applied in empirical work. To address this issue, we extend the conventional threshold regression model to the high-dimensional sparse settings and propose a sensible solution algorithm for this new class of models. We have proved that the parameter estimators are consistent and asymptotically normally distributed. As shown by Monte Carlo experiments, the high-dimensional sparse modeling methodology not only identifies the structural changes of the threshold model effectively, but also has good performance on the estimation of the important parameters.

Key words: High-Dimensional Threshold Model, Sparsity, Variable Selection, Parameter Estimation, Karush-Kuhn-Tucker Conditions