# Robust penalized spline estimation with difference penalties

arXiv: https://arxiv.org/abs/2012.13295 · HTML: https://mlsanity.com/paper/2012.13295/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Dec 2020.

## Built on by (most cited first, 1 of 1)

- [Maximum Correntropy Criterion Regression models with tending-to-zero scale parameters](https://mlsanity.com/paper/2110.12751/) (2021)

## Abstract (arXiv)

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.