| 讲座简介： | In modern economic studies, the population heterogeneity of multiple stratifications and the high dimensionality of the predictors pose a major challenge. In this study, we introduce an integrative procedure that can be used to explore the information regarding group and sparsity structures for high-dimensional and heterogeneous stratified models. Further, we propose $K$-regression modeling as a hybrid of complex and simple models exhibiting arbitrary dependence on the stratification features, but linear dependence on other variables. $K$-regression models preeminently exhibit the following features:(i) they are essentially non-parametric with respect to the stratified feature, and parametric linearly effects in other variables with potentially integrative pattern because the effects and the corresponding sparsity structures can be the same for the stratifications in common groups but vary across different groups; (ii) the devised $K$-regression algorithm can automatically integrate the stratifications pertaining to common regression model and simultaneously estimate the corresponding effects simultaneously; (iii) the proposal quickly recovers the subpopulation and sparsity structure of the $K$-regression models within massive and high-dimensional stratifications; (iv) the resulting estimators exhibit two-layer oracle properties, i.e., the oracle estimator obtained using the known group and sparsity structures is the local minimizer of the objective function with high probability. The stratification-specific bootstrap (SSB) sampling scheme was developed to improve the integration accuracy. Furthermore, the simulation studies provide supportive evidence that the newly proposed method performs appropriately in case of finite samples; a real data example has been provided for illustration. |
