Beyaztas Ufuk, Tez Mujgan, Lin Shang Han
Department of Statistics, Marmara University, Kadikoy-Istanbul, Turkey.
Department of Actuarial Studies and Business Analytics, Macquarie University, Sydney, Australia.
J Appl Stat. 2023 Apr 19;51(7):1359-1377. doi: 10.1080/02664763.2023.2202464. eCollection 2024.
Compared with the conditional mean regression-based scalar-on-function regression model, the scalar-on-function quantile regression is robust to outliers in the response variable. However, it is susceptible to outliers in the functional predictor (called leverage points). This is because the influence function of the regression quantiles is bounded in the response variable but unbounded in the predictor space. The leverage points may alter the eigenstructure of the predictor matrix, leading to poor estimation and prediction results. This study proposes a robust procedure to estimate the model parameters in the scalar-on-function quantile regression method and produce reliable predictions in the presence of both outliers and leverage points. The proposed method is based on a functional partial quantile regression procedure. We propose a weighted partial quantile covariance to obtain functional partial quantile components of the scalar-on-function quantile regression model. After the decomposition, the model parameters are estimated via a weighted loss function, where the robustness is obtained by iteratively reweighting the partial quantile components. The estimation and prediction performance of the proposed method is evaluated by a series of Monte-Carlo experiments and an empirical data example. The results are compared favorably with several existing methods. The method is implemented in an R package robfpqr.
与基于条件均值回归的函数标量回归模型相比，函数标量分位数回归对响应变量中的异常值具有鲁棒性。然而，它易受函数预测变量（称为杠杆点）中的异常值影响。这是因为回归分位数的影响函数在响应变量中是有界的，但在预测变量空间中是无界的。杠杆点可能会改变预测变量矩阵的特征结构，导致估计和预测结果不佳。本研究提出了一种稳健的方法来估计函数标量分位数回归方法中的模型参数，并在存在异常值和杠杆点的情况下产生可靠的预测。所提出的方法基于函数偏分位数回归过程。我们提出了一种加权偏分位数协方差来获得函数标量分位数回归模型的函数偏分位数分量。分解后，通过加权损失函数估计模型参数，其中通过对偏分位数分量进行迭代重新加权来获得稳健性。通过一系列蒙特卡罗实验和一个实证数据示例对所提出方法的估计和预测性能进行了评估。结果与几种现有方法相比具有优势。该方法在R包robfpqr中实现。
