Nested Model Averaging on Solution Path for High-dimensional Linear Regression

TL;DR

This paper introduces a nested model averaging approach on the solution path for high-dimensional linear regression, combining regularized estimators like lasso and SLOPE to improve prediction accuracy.

Contribution

It proposes a novel nested model averaging method that integrates regularized estimators on the solution path, demonstrating improved performance over existing methods.

Findings

Nested model averaging with lasso and SLOPE outperforms competing methods.

The approach is effective in high-dimensional settings.

Real data analysis shows superior prediction of violent crime rates.

Abstract

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.