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A multivariate uniformity test for the case of unknown support

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Abstract

A test for the hypothesis of uniformity on a support S⊂ℝd 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.

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Authors and Affiliations

  1. Universidad Autónoma de Madrid, Madrid, Spain

    José R. Berrendero & Antonio Cuevas

  2. Universidad de Santiago de Compostela, Santiago de Compostela, Spain

    Beatriz Pateiro-López

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  1. José R. Berrendero
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  2. Antonio Cuevas
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  3. Beatriz Pateiro-López
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Correspondence to Beatriz Pateiro-López.

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Berrendero, J.R., Cuevas, A. & Pateiro-López, B. A multivariate uniformity test for the case of unknown support. Stat Comput 22, 259–271 (2012). https://doi.org/10.1007/s11222-010-9222-z

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  • DOI: https://doi.org/10.1007/s11222-010-9222-z

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