Nested model averaging on solution path for high-dimensional linear regression

We study the nested model averaging method on the solution path for a high-dimensional linear regression problem. In particular, we propose to combine model averaging with regularized estimators (e.g., lasso, elastic net, and Sorted L-One Penalized Estimation [SLOPE]) on the solution path for high-dimensional linear regression. In simulation studies, we first conduct a systematic investigation on the impact of predictor ordering on the behaviour of nested model averaging, and then show that nested model averaging with lasso, elastic net and SLOPE compares favourably with other competing methods, including the infeasible lasso, elastic, net and SLOPE with the tuning parameter optimally selected. A real data analysis on predicting the per capita violent crime in the United States shows outstanding performance of the nested model averaging with lasso.