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Robust estimation with modified Huber's function for functional linear models
Statistics ( IF 1.9 ) Pub Date : 2020-11-01 , DOI: 10.1080/02331888.2020.1862114
Xiong Cai 1 , Liugen Xue 1 , Zhaoliang Wang 2
Affiliation  

In this article, we consider a new robust estimation procedure for functional linear models with both slope function and functional predictor approximated by functional principal component basis functions. A modified Huber's function with tail function substituted by the exponential squared loss (ESL) is applied to the estimation procedure for achieving robustness against outliers. The tuning parameters of the new estimation method are data-driven, which enables us to reach better robustness and efficiency than other robust methods in the presence of outliers or heavy-tailed error distribution. We will show that the resulting estimator for the slope function achieves the optimal convergence rate as the least-squares estimator does in the classical functional linear regression. The convergence rate of the prediction in terms of conditional mean squared prediction error is also established. The proposed method is illustrated with simulation studies and a real data example.

中文翻译:

使用修正的 Huber 函数对函数线性模型进行鲁棒估计

在本文中,我们考虑了一种新的稳健估计程序,用于具有斜率函数和由函数主成分基函数近似的函数预测器的函数线性模型。将尾函数替换为指数平方损失 (ESL) 的修正 Huber 函数应用于估计过程,以实现对异常值的鲁棒性。新估计方法的调整参数是数据驱动的,这使我们能够在存在异常值或重尾误差分布的情况下达到比其他鲁棒方法更好的鲁棒性和效率。我们将证明斜率函数的结果估计量达到了最佳收敛速度,正如最小二乘估计量在经典函数线性回归中所做的那样。还建立了条件均方预测误差方面的预测收敛速度。所提出的方法通过模拟研究和真实数据示例进行了说明。
更新日期:2020-11-01
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