In this article, we consider a new robust estimation procedure for the partial functional linear model (PFLM) with the slope function approximated by spline basis functions. This robust estimation procedure applies a modified Huber’s function with tail function replaced by the exponential squared loss (ESL) to achieve robustness against outliers. A data-driven procedure is presented for selecting the tuning parameters of the new estimation method, which enables us to reach better robustness and efficiency than other methods in the presence of outliers or non-normal errors. We construct robust estimators of both parametric coefficients and function coefficient in the PFLM. Moreover, some asymptotic properties of the resulting estimators are established. The finite sample performance of our proposed method is studied through simulations and illustrated with a data example.

在本文中，我们考虑了部分函数线性模型（PFLM）的新的鲁棒估计程序，该函数的斜率函数由样条基函数近似。这种鲁棒的估计过程应用了修正的Huber函数，尾函数被指数平方损失（ESL）取代，从而获得了针对异常值的鲁棒性。提出了一种数据驱动程序，用于选择新估计方法的调整参数，这使我们在存在异常值或非正常错误的情况下，比其他方法具有更好的鲁棒性和效率。我们在PFLM中构造了参数系数和函数系数的鲁棒估计器。此外，建立了所得估计量的一些渐近性质。