On the maximal multivariate spacing extension and convexity tests
Résumé
The notion of multivariate spacings was introduced and studied by Deheuvels, P.
(1983) for data uniformly distributed on the unit cube. Later on, Janson, S. (1987) extended
the results to bounded sets, and obtained a very ne result, namely, he derived the exact
asymptotic distribution of the maximal spacing. These results have been very useful in many
statistical applications.
We extend Janson's result to the case where the data are generated from a positive,
bounded support Lipchitz continuous density function, and develop a convexity test for the
support of a distribution.
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