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Validity of the parametric bootstrap for goodness-of-fit testing in semiparametric models

Christian Genest, Bruno Rémillard (2008)

Annales de l'I.H.P. Probabilités et statistiques

In testing that a given distribution Pbelongs to a parameterized family 𝒫 , one is often led to compare a nonparametric estimateAn of some functional A of P with an element Aθn corresponding to an estimate θn of θ. In many cases, the asymptotic distribution of goodness-of-fit statistics derived from the process n1/2(An−Aθn) depends on the unknown distribution P. It is shown here that if the sequences An and θn of estimators are regular in some sense, a parametric bootstrap approach yields valid approximations...

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