Robust estimation with a modified Huber’s loss for partial functional linear models based on splines
- Resource Type
- Article
- Authors
- Cai Xiong; Xue Liugen; Lu Fei
- Source
- Journal of the Korean Statistical Society, 49(4), pp.1214-1237 Dec, 2020
- Subject
- 통계학
- Language
- English
- ISSN
- 2005-2863
1226-3192
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 modifed 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 efciency than other methods in the presence of outliers or non-normal errors. We construct robust estimators of both parametric coefcients and function coefcient in the PFLM. Moreover, some asymptotic properties of the resulting estimators are established. The fnite sample performance of our proposed method is studied through simulations and illustrated with a data example.