M-type penalized splines with auxiliary scale estimation
Abstract
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.
Cite
@article{arxiv.1906.08577,
title = {M-type penalized splines with auxiliary scale estimation},
author = {Ioannis Kalogridis and Stefan Van Aelst},
journal= {arXiv preprint arXiv:1906.08577},
year = {2021}
}