Authors:
Paul Deheuvels L.S.T.A., Université Pierre et Marie Curie (Paris VI), 7 avenue du Château, F 92340 Bourg-la-Reine, France

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Gérard Derzko 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 BC(u) = B(u)−6Cu(1−u) Σ01B(s)ds, where B(·) denotes a Brownian bridge, and C, a constant. The investigation of the class of Gaussian processes {BC(·): C ∈ ℝ} leads to some unexpected distributional identities such as B2(·)
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B(·). We discuss this and similar results in an extended framework.
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Periodica Mathematica Hungarica
Language English
Size B5
Year of
Foundation
1971
Volumes
per Year
2
Issues
per Year
4
Founder Bolyai János Matematikai Társulat - János Bolyai Mathematical Society
Founder's
Address
H-1055 Budapest, Hungary Falk Miksa u. 12.I/4.
Publisher Akadémiai Kiadó
Springer Nature Switzerland AG
Publisher's
Address
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible
Publisher
Chief Executive Officer, Akadémiai Kiadó
ISSN 0031-5303 (Print)
ISSN 1588-2829 (Online)

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