Integrative Analysis for High-Dimensional Stratified Models

Abstract

In modern economic studies, the population heterogeneity of multiple strata 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 stratum 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 strata in common groups but vary across different groups; (ii) the devised K-regression algorithm can automatically integrate the strata pertaining to common regression model and simultaneously estimate the corresponding effects simultaneously; (iii) the proposal quickly 1