Robust Regression Shrinkage and Consistent Variable Selection Through the LAD-Lasso
结合最小绝对偏差回归与Lasso方法，提出LAD-lasso，能同时进行参数估计和变量选择，且对重尾误差或异常值具有稳健性，估计量具有渐近有效性。
The least absolute deviation (LAD) regression is a useful method for robust regression, and the least absolute shrinkage and selection operator (lasso) is a popular choice for shrinkage estimation and variable selection. In this article we combine these two classical ideas together to produce LAD-lasso. Compared with the LAD regression, LAD-lasso can do parameter estimation and variable selection simultaneously. Compared with the traditional lasso, LAD-lasso is resistant to heavy-tailed errors or outliers in the response. Furthermore, with easily estimated tuning parameters, the LAD-lasso estimator enjoys the same asymptotic efficiency as the unpenalized LAD estimator obtained under the true model (i.e., the oracle property). Extensive simulation studies demonstrate satisfactory finite-sample performance of LAD-lasso, and a real example is analyzed for illustration purposes.