# M-type penalized splines with auxiliary scale estimation

arXiv: https://arxiv.org/abs/1906.08577 · HTML: https://mlsanity.com/paper/1906.08577/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Jun 2019.

## 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 smoothing is a popular and flexible method of obtaining estimates in nonparametric regression but the classical least-squares criterion is highly susceptible to model deviations and atypical observations. Penalized spline estimation with a resistant loss function is a natural remedy, yet to this day the asymptotic properties of M-type penalized spline estimators have not been studied. We show in this paper that M-type penalized spline estimators achieve the same rates of convergence as their least-squares counterparts, even with auxiliary scale estimation. We further find theoretical justification for the use of a small number of knots relative to the sample size. We illustrate the benefits of M-type penalized splines in a Monte-Carlo study and two real-data examples, which contain atypical observations.