Bootstrap in functional linear regression

被引：28
|
作者：
Gonzalez-Manteiga, Wenceslao [1 ]
Martinez-Calvo, Adela [1 ]
机构：
[1] Univ Santiago de Compostela, Fac Matemat, Dept Estat & IO, Santiago De Compostela 15782, A Coruna, Spain
来源：
JOURNAL OF STATISTICAL PLANNING AND INFERENCE | 2011年 / 141卷 / 01期
关键词：
Bootstrap; Confidence interval; Functional linear model; Functional principal components analysis; CONVERGENCE; PREDICTION;
D O I：
10.1016/j.jspi.2010.06.027
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：
We have considered the functional linear model with scalar response and functional explanatory variable. One of the most popular methodologies for estimating the model parameter is based on functional principal components analysis (FPCA). In recent literature, weak convergence for a wide class of FPCA-type estimates has been proved, and consequently asymptotic confidence sets can be built. In this paper, we have proposed an alternative approach in order to obtain pointwise confidence intervals by means of a bootstrap procedure, for which we have obtained its asymptotic validity. Besides, a simulation study allows us to compare the practical behaviour of asymptotic and bootstrap confidence intervals in terms of coverage rates for different sample sizes. (C) 2010 Elsevier B.V. All rights reserved.
引用
收藏
页码：453 / 461
页数：9
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