The Risk of James–Stein and Lasso Shrinkage
比较了普通最小二乘、詹姆斯-斯坦和Lasso三种估计量在线性回归中的均方误差,发现Lasso对参数设定敏感且部分情况下劣于OLS,提醒研究者注意其潜在陷阱。
This article compares the mean-squared error (or ℓ2 risk) of ordinary least squares (OLS), James–Stein, and least absolute shrinkage and selection operator (Lasso) shrinkage estimators in simple linear regression where the number of regressors is smaller than the sample size. We compare and contrast the known risk bounds for these estimators, which shows that neither James–Stein nor Lasso uniformly dominates the other. We investigate the finite sample risk using a simple simulation experiment. We find that the risk of Lasso estimation is particularly sensitive to coefficient parameterization, and for a significant portion of the parameter space Lasso has higher mean-squared error than OLS. This investigation suggests that there are potential pitfalls arising with Lasso estimation, and simulation studies need to be more attentive to careful exploration of the parameter space.