Bootstrap Calibration in Functional Linear Regression Models with Applications

Wenceslao González-Manteiga () and Adela Martínez-Calvo ()
Additional contact information
Wenceslao González-Manteiga: Universidad de Santiago de Compostela, Departamento de Estadística e I.O., Facultad de Matemáticas
Adela Martínez-Calvo: Universidad de Santiago de Compostela, Departamento de Estadística e I.O., Facultad de Matemáticas

A chapter in Proceedings of COMPSTAT'2010, 2010, pp 199-207 from Springer

Abstract: Abstract Our work focuses on the functional linear model given by $$Y=\langle\theta,X\rangle+\epsilon,$$ where Y and ε are real random variables, X is a zero-mean random variable valued in a Hilbert space $$(\mathcal{H},\langle\cdot,\cdot\rangle)$$ , and $$\theta\in\mathcal{H}$$ is the fixed model parameter. Using an initial sample $$\{(X_i,Y_i)\}_{i=1}^n$$ , a bootstrap resampling $$Y_i^{*}=\langle\hat{\theta},X_i\rangle+\hat{\epsilon}_i^{*}$$ , $$i=1,\ldots,n$$ , is proposed, where $$\hat{\theta}$$ is a general pilot estimator, and $$\hat{\epsilon}_i^{*}$$ is a naive or wild bootstrap error. The obtained consistency of bootstrap allows us to calibrate distributions as $$P_X\{\sqrt{n}(\langle\hat{\theta},x\rangle-\langle\theta,x\rangle)\leq y\}$$ for a fixed x, where P X is the probability conditionally on $$\{X_i\}_{i=1}^n$$ . Different applications illustrate the usefulness of bootstrap for testing different hypotheses related with θ, and a brief simulation study is also presented.

Keywords: bootstrap; functional linear regression; functional principal components analysis; hypothesis test (search for similar items in EconPapers)
Date: 2010
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-7908-2604-3_18

Ordering information: This item can be ordered from
http://www.springer.com/9783790826043

DOI: 10.1007/978-3-7908-2604-3_18

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().