On the validity of the bootstrap in nonparametric functional regression
(2008) , 24 pages
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- Abstract
- We consider the functional nonparametric regression model Y = r(X)+", where the response Y is univariate, X is a functional covariate (i.e. valued in some infinite-dimensional space), and the error " satisfies E("|X) = 0. For this model, the point-wise asymptotic normality of a kernel estimator br(·) of r(·) has been proved in the literature. In order to use this result for building pointwise confidence intervals for r(·), the asymptotic variance and bias of br(·) 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 br(·) − r(·). 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 in order to compute pointwise confidence intervals.
- Affiliations
Université Paul Sabatier Institut de Mathématique
Citations
Ferraty, F., Van Keilegom, I., & Vieu, P. (2008). On the validity of the bootstrap in nonparametric functional regression (STAT Discusion Paper 0818). https://hdl.handle.net/2078.5/33862