Local roughness penalties for regression splines

被引：7

作者：

Cardot, H ^{[1
]}

机构：

[1] INRA, Unite Biometrie & Intelligence Artificielle, F-30326 Castanet Tolosan, France

来源：

COMPUTATIONAL STATISTICS | 2002年 / 17卷 / 01期

关键词：

local roughness penalties; spatially adaptive estimators; regression splines; convergence;

D O I：

10.1007/s001800200092

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：

This paper introduces a new nonparametric estimator of the regression based on penalized regression splines. Local roughness penalties that rely on local support properties of B-splines are introduced in order to deal with the spatial heterogeneity of the function to be estimated. This estimator is shown to attain optimal rates of convergence. Then its good performances are confirmed on a simulation study.

引用

页码：89 / 102

页数：14

共 17 条

[1] ASYMPTOTIC INTEGRATED MEAN-SQUARE ERROR USING LEAST-SQUARES AND BIAS MINIMIZING SPLINES [J].

AGARWAL, GG ;

STUDDEN, WJ .

ANNALS OF STATISTICS, 1980, 8 (06) :1307-1325

[2] Simultaneous non-parametric regressions of unbalanced longitudinal data [J].

Besse, PC ;

Cardot, H ;

Ferraty, F .

COMPUTATIONAL STATISTICS & DATA ANALYSIS, 1997, 24 (03) :255-270

[3] NONPARAMETRIC-ESTIMATION OF A REGRESSION FUNCTION [J].

BURMAN, P ;

CHEN, KW .

ANNALS OF STATISTICS, 1989, 17 (04) :1567-1596

[4] Nonparametric estimation of smoothed principal components analysis of sampled noisy functions [J].

Cardot, H .

JOURNAL OF NONPARAMETRIC STATISTICS, 2000, 12 (04) :503-538

[5]

de Boor C., 1978, PRACTICAL GUIDE SPLI, DOI DOI 10.1007/978-1-4612-6333-3

[6] Automatic Bayesian curve fitting [J].

Denison, DGT ;

Mallick, BK ;

Smith, AFM .

JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY, 1998, 60 :333-350

[7] A nonparametric test of the non-convexity of regression [J].

Diack, CAT ;

Thomas-Agnan, C .

JOURNAL OF NONPARAMETRIC STATISTICS, 1998, 9 (04) :335-362

[8]

DIERCKX P., 1993, Monographs on Numerical Analysis

[9] Flexible smoothing with B-splines and penalties [J].

Eilers, PHC ;

Marx, BD .

STATISTICAL SCIENCE, 1996, 11 (02) :89-102

[10] MULTIVARIATE ADAPTIVE REGRESSION SPLINES [J].

FRIEDMAN, JH .

ANNALS OF STATISTICS, 1991, 19 (01) :1-67

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