Bootstrap test of goodness of fit to a linear model when errors are correlated
Titel:
Bootstrap test of goodness of fit to a linear model when errors are correlated
Auteur:
Fernandez, J. M. Vilar Manteiga, W. Gonzalez
Verschenen in:
Communications in statistics
Paginering:
Jaargang 25 (1966) nr. 12 pagina's 2925-2953
Jaar:
1966
Inhoud:
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(mˆn, At(.)θn), between mˆn, 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.
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