2020/12/31 by Ioannis Kalogridis, Stefan Van Aelst
Engineering · Mathematics · #Advanced Statistical Methods and Models #Applied mathematics #Control Systems and Identification #Estimator #Least-squares function approximation #Mathematical optimization #Mathematics #Spline (mechanical) #Statistical Methods and Inference #Statistics #msc:62G08 #msc:62G20 #msc:62G35 #stat.ME
paper · pdf · doi:10.1016/j.ecosta.2021.07.005
published as Econometrics and Statistics, 2021
arxiv created 2021/07/19 · openalex publication_date 2021/07/23 · arxiv updated 2022/03/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Penalized spline estimation with discrete difference penalties (P-splines) is a popular estimation method for semiparametric models, but the classical least-squares estimator is highly sensitive to deviations from its ideal model assumptions. To remedy this deficiency, a broad class of P-spline estimators based on general loss functions is introduced and studied. Robust estimators are obtained by well-chosen loss functions, such as the Huber or Tukey loss function. A preliminary scale estimator can also be included in the loss function. It is shown that this class of P-spline estimators enjoys the same optimal asymptotic properties as least-squares P-splines, thereby providing strong theoretical motivation for its use. The proposed estimators may be computed very efficiently through a simple adaptation of well-established iterative least squares algorithms and exhibit excellent performance even in finite samples, as evidenced by a numerical study and a real-data example.