Robust estimation of regression models with potentially endogenous outliers via a modern optimization lens
针对线性回归模型中可能存在的内生异常值问题，提出基于L0正则化的局部组合搜索算法，通过蒙特卡洛模拟和股票收益预测应用证明其相比L1正则化方法能有效降低偏差、提高预测精度，并提供了R语言工具包。
.This article addresses the robust estimation of linear regression models in the presence of potentially endogenous outliers. Through Monte Carlo simulations, we demonstrate that existing methods using L1-regularization on case-specific parameters, including the Huber estimator and the least absolute deviation (LAD) estimator, exhibit significant bias when outliers are endogenous. Motivated by this finding, we investigate L0-regularized estimation methods. We propose systematic heuristic algorithms, notably a local combinatorial search refinement based on the iterative hard-thresholding solution, to solve the combinatorial optimization problem of the L0-regularized estimation efficiently. Our Monte Carlo simulations yield two key results: (i) The local combinatorial search algorithm substantially improves solution quality compared to the initial projection-based hard-thresholding algorithm while offering greater computational efficiency than directly solving the original optimization problem; (ii) The L0-regularized estimator demonstrates superior performance in terms of bias reduction, estimation accuracy, and out-of-sample prediction errors compared to L1-regularized alternatives. In the stock return forecasting application, our method identifies the crisis periods across rolling windows and improves the prediction accuracy over baseline methods. An accompanying R package is provided for practitioners.