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  • 1 L.S.T.A., Université Pierre et Marie Curie (Paris VI), 7 avenue du Château, F 92340 Bourg-la-Reine, France
  • 2 Recherche et Développement, L.S.T.A., Université Paris VI and Sanofi-Aventis, 371 rue du Professeur Joseph Blayac, 34184 Montpellier, Cedex 04, France
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Abstract  

We consider an empirical process based upon ratios of selected pairs of spacings, generated by independent samples of arbitrary sizes. As a main result, we show that when both samples are uniformly distributed on (possibly shifted) intervals of equal lengths, this empirical process converges to a mean-centered Brownian bridge of the form B C(u) = B(u)−6Cu(1−u) Σ0 1 B(s)ds, where B(·) denotes a Brownian bridge, and C, a constant. The investigation of the class of Gaussian processes {B C(·): C ∈ ℝ} leads to some unexpected distributional identities such as B 2(·)

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B(·). We discuss this and similar results in an extended framework.