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.

中文翻译：

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高维线性回归在求解路径上的嵌套模型平均

我们研究高维线性回归问题在求解路径上的嵌套模型平均方法。尤其是，我们建议在求解路径上将模型平均与正则化估计量（例如套索，弹性网和排序的L一罚估计[SLOPE]）结合起来，以进行高维线性回归。在模拟研究中，我们首先对预测变量顺序对嵌套模型平均行为的影响进行系统的调查，然后证明以套索，弹性网和SLOPE进行嵌套模型平均与其他竞争方法（包括不可行的套索）相比具有优势，弹性，网状和斜率，并优化选择了调整参数。对美国人均暴力犯罪进行预测的真实数据分析显示，套索模型平均具有套索的出色表现。