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Le Cam spacings theorem in dimension two

Lionel Cucala
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Abstract

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.

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Lionel Cucala. 2005-07-18. Le Cam spacings theorem in dimension two. https://arxiv.org/abs/math/0507367

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