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The most general sequence, with Gumbel margins, generated by maxima procedures in an auto-regressive way (one step) is defined constructively and its properties obtained; some remarks for statistical estimation are presented.
The purpose of this paper is to study the asymptotic choice between two models {F(x|α), α ∈ A ⊆ R} and {G(x|β), β ∈ B ⊆ R}, A and B being intervals but such that for (α, β}, and only for this pair, we have F(x|α) = G(x|β).
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