弹性约束估计的显著性检验及其渐近分布

A significance test for the elastic net and its asymptotic distribution with general predictors

本文基于高维稀疏线性模型,研究弹性约束估计(elastic net, EN)的相关显著性检验问题,在弹性约束估计的解路径上建立Cov-EN检验.为了获取该检验的理论结果,本文回顾KKT (KarushKuhn-Tucker)条件,通过Lars算法计算得到弹性约束估计的解路径上每个节点的解析表达式,证明该检验在一般数据下渐近收敛于参数为1的指数分布.本文的数值模拟和实证分析进一步阐述Cov-EN检验的特点与作用,并与Lasso的协方差检验进行比较.

This paper considers the significance test for the elastic net in high dimensional sparse linear regression models. A test statistic called Cov-EN test statistic is proposed which is based on the knots of the elastic net solution path. It is shown to have an Exp(1) asymptotic distribution with general predictors. To prepare for the test statistic, we review KKT conditions and compute each knot of Lars algorithm for the elastic net solution path. Simulations and real examples given in this paper illustrate the performance of the Cov-EN test statistic and compare the results with the significance test for the Lasso.