In this paper, we study ultra-high-dimensional partially linear models when the dimension of thelinear predictors grows exponentially with the sample size. For the variable screening, we proposea sequential profile La...In this paper, we study ultra-high-dimensional partially linear models when the dimension of thelinear predictors grows exponentially with the sample size. For the variable screening, we proposea sequential profile Lasso method (SPLasso) and show that it possesses the screening property.SPLasso can also detect all relevant predictors with probability tending to one, no matter whetherthe ultra-high models involve both parametric and nonparametric parts. To select the best subset among the models generated by SPLasso, we propose an extended Bayesian information criterion (EBIC) for choosing the final model. We also conduct simulation studies and apply a realdata example to assess the performance of the proposed method and compare with the existingmethod.展开更多
基金Gaorong Li’s research was supported in part by the National Natural Science Foundation of China[number 11471029]Tiejun Tong’s research was supported in part by the National Natural Science Foundation of China[number 11671338]+1 种基金the Hong Kong Baptist University grants[grant number FRG2/15-16/019][grant number FRG1/16-17/018].
文摘In this paper, we study ultra-high-dimensional partially linear models when the dimension of thelinear predictors grows exponentially with the sample size. For the variable screening, we proposea sequential profile Lasso method (SPLasso) and show that it possesses the screening property.SPLasso can also detect all relevant predictors with probability tending to one, no matter whetherthe ultra-high models involve both parametric and nonparametric parts. To select the best subset among the models generated by SPLasso, we propose an extended Bayesian information criterion (EBIC) for choosing the final model. We also conduct simulation studies and apply a realdata example to assess the performance of the proposed method and compare with the existingmethod.
