Le Cam spacings theorem in dimension two

Lionel Cucala (1, 2)

1 LSP - Laboratoire de Statistique et Probabilités
2 GREMAQ - Groupe de recherche en économie mathématique et quantitative

The definition of spacings associated to a sequence of random variables is extended to the case of random vectors in [0,1]^2. Beirlant & al. (1991) give an alternative proof of the Le Cam (1958) theorem concerning asymptotic normality of additive functions of uniform spacings in [0,1]. I adapt their technique to the two-dimensional case, leading the way to new directions in the domain of Complete Spatial Randomness (CSR) testing.

Mots clés: uniform spacings; spatial point patterns; complete spatial randomness

Domaines: Statistiques [math.ST]

Lionel Cucala. Le Cam spacings theorem in dimension two. Annales de l'ISUP, 2005, XLIX (2-3), pp.41-55. ⟨hal-00007571v2⟩