Abstract

A robust estimator is proposed for the parameters that characterize the linear regression problem. It is based on the notion of shrinkages, often used in Finance and previously studied for outlier detection in multivariate data. A thorough simulation study is conducted to investigate: the efficiency with Normal and heavy-tailed errors, the robustness under contamination, the computational time, the affine equivariance and breakdown value of the regression estimator. Two classical data-sets often used in the literature and a real socioeconomic data-set about the Living Environment Deprivation of areas in Liverpool (UK), are studied. The results from the simulations and the real data examples show the advantages of the proposed robust estimator in regression.

中文翻译：

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基于收缩的稳健回归及其在生活环境剥夺中的应用

摘要

针对表征线性回归问题的参数，提出了一种鲁棒的估计器。它基于收缩的概念，通常在财务中使用，并且先前已经研究过收缩以用于多元数据的异常检测。进行了全面的仿真研究，以调查：具有正尾误差的效率，污染下的鲁棒性，计算时间，仿射等方差和回归估计器的分解值。研究了文献中经常使用的两个经典数据集，以及有关英国利物浦地区生活环境匮乏的真实社会经济数据集。仿真和实际数据示例的结果表明了所提出的鲁棒估计器在回归中的优势。