Local linear regression for functional predictor and scalar response

被引：100

作者：

Baillo, Amparo ^{[1
]}

Grane, Aurea ^{[2
]}

机构：

[1] Univ Autonoma Madrid, Dept Anal Econ Econ Cuantitat, E-28049 Madrid, Spain

[2] Univ Carlos III Madrid, Dept Estadist, Getafe Madrid 28903, Spain

来源：

JOURNAL OF MULTIVARIATE ANALYSIS | 2009年 / 100卷 / 01期

关键词：

Functional data; Nonparametric smoothing; Local linear regression; Kernel regression; Fourier expansion; Cross-validation; MODELS;

D O I：

10.1016/j.jmva.2008.03.008

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：

The aim of this work is to introduce a new nonparametric regression technique in the context of functional covariate and scalar response. We propose a local linear regression estimator and study its asymptotic behaviour. Its finite-sample performance is compared with a Nadayara-Watson type kernel regression estimator and with the linear regression estimator via a Monte Carlo study and the analysis of two real data sets. In all the scenarios considered, the local linear regression estimator performs better than the kernel one, in the sense that the mean squared prediction error is lower. (C) 2008 Elsevier Inc. All rights reserved.

引用

页码：102 / 111

页数：10

共 19 条

[11] Fractal dimensionality and regression estimation in semi-normed vectorial spaces [J].

Ferraty, F ;

Vieu, P .

COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 2000, 330 (02) :139-142

[12] Functional sliced inverse regression analysis [J].

Ferré, L ;

Yao, AF .

STATISTICS, 2003, 37 (06) :475-488

[13] Methodology and convergence rates for functional linear regression [J].

Hall, Peter ;

Horowitz, Joel L. .

ANNALS OF STATISTICS, 2007, 35 (01) :70-91

[14] Generalized linear models with functional predictors [J].

James, GM .

JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY, 2002, 64 :411-432

[15] Generalized functional linear models [J].

Müller, HG ;

Stadtmüller, U .

ANNALS OF STATISTICS, 2005, 33 (02) :774-805

[16]

Ramsay J., 2005, FUNCTIONAL DATA ANAL

[17] MULTIVARIATE LOCALLY WEIGHTED LEAST-SQUARES REGRESSION [J].

RUPPERT, D ;

WAND, MP .

ANNALS OF STATISTICS, 1994, 22 (03) :1346-1370

[18]

Wand M. P., 1995, KERNEL SMOOTHING

[19]

Zygmund A., 1988, TRIGONOMETRIC SERIES

← 1 2 →