Nested Model Averaging on Solution Path for High-dimensional Linear Regression
This work addresses model selection and prediction accuracy in high-dimensional statistics, offering an incremental improvement for researchers and practitioners in fields like criminology and data science.
The paper tackles high-dimensional linear regression by proposing nested model averaging with regularized estimators like lasso and SLOPE on the solution path, showing in simulations that it outperforms competing methods, including optimally tuned infeasible versions, and achieves outstanding performance in a real-world crime prediction dataset.
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 and 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 behavior of nested model averaging, then show that nested model averaging with lasso and SLOPE compares favorably with other competing methods, including the infeasible lasso and SLOPE with the tuning parameter optimally selected. A real data analysis on predicting the per capita violent crime in the United States shows an outstanding performance of the nested model averaging with lasso.