2017
DOI: 10.1007/s10687-017-0284-6
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A generalization of the maximal-spacings in several dimensions and a convexity test.

Abstract: The notion of maximal-spacing in several dimensions was introduced and studied by Deheuvels (1983) for data uniformly distributed on the unit cube. Later on, Janson (1987) extended the results to data uniformly distributed on any bounded set, and obtained a very fine result, namely, he derived the asymptotic distribution of different maximal-spacings notions. These results have been very useful in many statistical applications.We extend Janson's results to the case where the data are generated from a Hölder co… Show more

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Cited by 7 publications
(25 citation statements)
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“…In this way, it distinguishes between low and high density regions. Throughout this paper, Janson (1987) calibrated the volume of the maximal spacing under uniformity assumptions without conditions on the shape of the support S. The corresponding extension established in Theorem 2 in Aaron et al (2017) is shown in Theorem 1 modifying slightly the original hypotheses on f and on the shape of S. The result remains true if it is assumed that S is under (R) and the density function f satisfies ( f L 0,1 ):…”
Section: About Maximal Spacingsmentioning
confidence: 91%
See 4 more Smart Citations
“…In this way, it distinguishes between low and high density regions. Throughout this paper, Janson (1987) calibrated the volume of the maximal spacing under uniformity assumptions without conditions on the shape of the support S. The corresponding extension established in Theorem 2 in Aaron et al (2017) is shown in Theorem 1 modifying slightly the original hypotheses on f and on the shape of S. The result remains true if it is assumed that S is under (R) and the density function f satisfies ( f L 0,1 ):…”
Section: About Maximal Spacingsmentioning
confidence: 91%
“…The notion of maximal-spacing in several dimensions was introduced and studied by Deheuvels (1983) for uniformly distributed data on the unit cube. Later on, Janson (1987) extended these results to uniformly distributed data on any bounded set and derived the asymptotic distribution of different maximal-spacings notions without conditions on the shape of the support S. Aaron et al (2017) generalized the results by Janson (1987) to the non-uniform case.…”
Section: About Maximal Spacingsmentioning
confidence: 97%
See 3 more Smart Citations