Abstract
Given the regression model Yi = m(xi) +εi (xi ε C, i = l,…,n, C a compact set in R) where m is unknown and the random errors {εi} present an ARMA structure, we design a bootstrap method for testing the hypothesis that the regression function follows a general linear model: Ho : m ε {mθ(.) = At(.)θ : θ ε ⊝ ⊂ Rq} with A a functional from R to Rq. The criterion of the test derives from a Cramer-von-Mises type functional distance D = d2([mcirc]n, At(.)θn), between [mcirc]n, a Gasser-Miiller non-parametric estimator of m, and the member of the class defined in Ho that is closest to mn in terms of this distance. The consistency of the bootstrap distribution of D and θn is obtained under general conditions. Finally, simulations show the good behavior of the bootstrap approximation with respect to the asymptotic distribution of D = d2.