On the Validity of the Bootstrap in Non‐Parametric Functional Regression

Frédéric Ferraty, Ingrid Van Keilegom () and Philippe Vieu

Scandinavian Journal of Statistics, 2010, vol. 37, issue 2, 286-306

Abstract: Abstract. We consider the functional non‐parametric regression model Y= r(χ)+ɛ, where the response Y is univariate, χ is a functional covariate (i.e. valued in some infinite‐dimensional space), and the error ɛ satisfies E(ɛ | χ) = 0. For this model, the pointwise asymptotic normality of a kernel estimator of r (·) has been proved in the literature. To use this result for building pointwise confidence intervals for r (·), the asymptotic variance and bias of need to be estimated. However, the functional covariate setting makes this task very hard. To circumvent the estimation of these quantities, we propose to use a bootstrap procedure to approximate the distribution of . Both a naive and a wild bootstrap procedure are studied, and their asymptotic validity is proved. The obtained consistency results are discussed from a practical point of view via a simulation study. Finally, the wild bootstrap procedure is applied to a food industry quality problem to compute pointwise confidence intervals.

Date: 2010
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (22)

Downloads: (external link)
https://doi.org/10.1111/j.1467-9469.2009.00662.x

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:bla:scjsta:v:37:y:2010:i:2:p:286-306

Ordering information: This journal article can be ordered from
http://www.blackwell ... bs.asp?ref=0303-6898

Access Statistics for this article

Scandinavian Journal of Statistics is currently edited by ÿrnulf Borgan and Bo Lindqvist

More articles in Scandinavian Journal of Statistics from Danish Society for Theoretical Statistics, Finnish Statistical Society, Norwegian Statistical Association, Swedish Statistical Association
Bibliographic data for series maintained by Wiley Content Delivery ().