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Statistics and Computing

, Volume 22, Issue 1, pp 259–271 | Cite as

A multivariate uniformity test for the case of unknown support

  • José R. Berrendero
  • Antonio Cuevas
  • Beatriz Pateiro-LópezEmail author
Article

Abstract

A test for the hypothesis of uniformity on a support S⊂ℝ d is proposed. It is based on the use of multivariate spacings as those studied in Janson (Ann. Probab. 15:274–280, 1987). As a novel aspect, this test can be adapted to the case that the support S is unknown, provided that it fulfils the shape condition of λ-convexity. The consistency properties of this test are analyzed and its performance is checked through a small simulation study. The numerical problems involved in the practical calculation of the maximal spacing (which is required to obtain the test statistic) are also discussed in some detail.

Keywords

Uniformity Set estimation Multidimensional spacings 

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • José R. Berrendero
    • 1
  • Antonio Cuevas
    • 1
  • Beatriz Pateiro-López
    • 2
    Email author
  1. 1.Universidad Autónoma de MadridMadridSpain
  2. 2.Universidad de Santiago de CompostelaSantiago de CompostelaSpain

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