arXiv 7 Aug 2024 · Econometrics · publishedEconometric Reviews (2025) · 1 citations (OpenAlex)
arXiv:2408.03930 · PDF · DOI · OpenAlex · Extracted main text
This paper addresses the robust estimation of linear regression models in the presence of potentially endogenous outliers. Through Monte Carlo simulations, we demonstrate that existing $L_1$-regularized estimation methods, including the Huber estimator and the least absolute deviation (LAD) estimator, exhibit significant bias when outliers are endogenous. Motivated by this finding, we investigate $L_0$-regularized estimation methods. We propose systematic heuristic algorithms, notably an iterative hard-thresholding algorithm and a local combinatorial search refinement, to solve the combinatorial optimization problem of the \(L_0\)-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 mixed integer optimization problem. (ii) The $L_0$-regularized estimator demonstrates superior performance in terms of bias reduction, estimation accuracy, and out-of-sample prediction errors compared to $L_1$-regularized alternatives. We illustrate the practical value of our method through an empirical application to stock return forecasting.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Thompson, R (2022) Robust subset selection | 0.874 | 8 | 2 | 100% |
| 2 | Bertsimas, D., A. King, and R. Mazumder (2016) Best subset selection via a modern optimization lens | 0.874 | 6 | 2 | 100% |
| 3 | Hazimeh, H. and R. Mazumder (2020) Fast best subset selection: Coordinate descent and local combinatorial optimization algorithms | 0.874 | 5 | 2 | 100% |
| 4 | She, Y. and A. B. Owen (2011) Outlier detection using nonconvex penalized regression | 0.811 | 4 | 2 | 100% |
| 5 | Lee, J. H., Z. Shi, and Z. Gao (2022) On lasso for predictive regression | 0.737 | 3 | 2 | 100% |
| 6 | Welch, I. and A. Goyal (2008) A comprehensive look at the empirical performance of equity premium prediction | 0.737 | 3 | 2 | 100% |
| 7 | Gurobi Optimization, LLC (2024) Gurobi Optimizer Reference Manual | 0.644 | 2 | 2 | 100% |
| 8 | Huber, P. J (1964) Robust estimation of a location parameter | 0.644 | 2 | 2 | 100% |
| 9 | Huber, P. J. and D. Donoho (1983) The notion of breakdown point | 0.644 | 2 | 2 | 100% |
| 10 | Koo, B., H. M. Anderson, M. H. Seo, and W. Yao (2020) High-dimensional predictive regression in the presence of cointegration | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 21 scored citations.