Resumen de Bootstrap in semi-functional partial linear regression under dependence

Germán Aneiros Pérez , Paula Raña Míguez, Philippe Vieu , Juan Manuel Vilar Fernández

• This paper deals with the semi-functional partial linear regression model Y=XXTββ+m(χχ)+ε under α -mixing conditions. ββ∈Rp and m(⋅) denote an unknown vector and an unknown smooth real-valued operator, respectively. The covariates XX and χχ are valued in Rp and some infinite-dimensional space, respectively, and the random error ε verifies E(ε|XX,χχ)=0 . Naïve and wild bootstrap procedures are proposed to approximate the distribution of kernel-based estimators of ββ and m(χ) , and their asymptotic validities are obtained. A simulation study shows the behavior (on finite sample sizes) of the proposed bootstrap methodology when applied to construct confidence intervals, while an application to real data concerning electricity market illustrates its usefulness in practice.