M-type penalized splines with auxiliary scale estimation

被引：4

作者：

Kalogridis, Ioannis ^{[1
]}

Van Aelst, Stefan ^{[1
]}

机构：

[1] Katholieke Univ Leuven, Dept Math, Celestijnenlaan 200B, B-3001 Leuven, Belgium

来源：

JOURNAL OF STATISTICAL PLANNING AND INFERENCE | 2021年 / 212卷

关键词：

Penalized splines; M-estimation; Auxiliary scale; Asymptotics; ASYMPTOTICS; REGRESSION; CONVERGENCE; RATES;

D O I：

10.1016/j.jspi.2020.09.004

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

Penalized spline regression is a popular and flexible method of obtaining estimates in nonparametric models 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 illustrate the benefits of M-type penalized splines in a Monte-Carlo study and two real-data examples, which contain atypical observations. (C) 2020 Elsevier B.V. All rights reserved.

引用

页码：97 / 113

页数：17

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