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Robust estimation for semi-functional linear regression models
Computational Statistics & Data Analysis ( IF 1.8 ) Pub Date : 2020-12-01 , DOI: 10.1016/j.csda.2020.107041
Graciela Boente , Matías Salibian-Barrera , Pablo Vena

Abstract Semi-functional linear regression models postulate a linear relationship between a scalar response and a functional covariate, and also include a non-parametric component involving a univariate explanatory variable. It is of practical importance to obtain estimators for these models that are robust against high-leverage outliers, which are generally difficult to identify and may cause serious damage to least squares and Huber-type M -estimators. For that reason, robust estimators for semi-functional linear regression models are constructed combining B -splines to approximate both the functional regression parameter and the nonparametric component with robust regression estimators based on a bounded loss function and a preliminary residual scale estimator. Consistency and rates of convergence for the proposed estimators are derived under mild regularity conditions. The reported numerical experiments show the advantage of the proposed methodology over the classical least squares and Huber-type M -estimators for finite samples. The analysis of real examples illustrates that the robust estimators provide better predictions for non-outlying points than the classical ones, and that when potential outliers are removed from the training and test sets both methods behave very similarly.

中文翻译:

半函数线性回归模型的稳健估计

摘要 半函数线性回归模型假定标量响应和函数协变量之间存在线性关系,并且还包括涉及单变量解释变量的非参数组件。获得这些模型的估计量具有实际重要性,这些估计量对高杠杆异常值具有鲁棒性,这些异常值通常难以识别并且可能对最小二乘法和 Huber 型 M 估计量造成严重损害。出于这个原因,半函数线性回归模型的鲁棒估计器是结合 B 样条构建的,以基于有界损失函数和初步残差尺度估计器的鲁棒回归估计器来近似函数回归参数和非参数分量。建议的估计器的一致性和收敛速度是在温和的规律性条件下得出的。报告的数值实验显示了所提出的方法优于经典最小二乘法和用于有限样本的 Huber 型 M 估计器。对真实示例的分析表明,鲁棒估计器对非外围点提供了比经典估计器更好的预测,并且当从训练和测试集中去除潜在的异常值时,两种方法的行为非常相似。
更新日期:2020-12-01
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