论文标题
半功能线性回归模型的强大估计
Robust estimation for semi-functional linear regression models
论文作者
论文摘要
半功能线性回归模型假定标量响应与功能协变量之间的线性关系，还包括涉及单变量解释变量的非参数分量。对于这些模型的估计值非常重要，这些模型与高杠杆异常值具有牢固的估计，这些异常值通常很难识别，并且可能对最小二乘和Huber型$ M $ $估计器造成严重损害。因此，半功能线性回归模型的可靠估计器组合结合了$ b $ splines，以近似基于有界损耗函数和初步的残基量表估计器，近似具有鲁棒回归估计器的功能回归参数和非参数组件。提出的估计量的一致性和收敛速率在轻度的规律性条件下得出。报道的数值实验表明，所提出的方法比经典的最小二乘和huber型$ m $估计器用于有限样品的优点。对真实示例的分析表明，强大的估计器比经典的估计器为非出行点提供了更好的预测，并且当从训练中删除潜在异常值和测试集时，两种方法的行为都非常相似。
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 illustrate 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.
