A multivariate uniformity test for the case of unknown support
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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.
KeywordsUniformity Set estimation Multidimensional spacings
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- Baddeley, A., Turner, R.: Spatstat: an R package for analyzing spatial point patterns. J. Stat. Softw. 6, 1–42 (2005) Google Scholar
- Delaunay, B.: Sur la sphere vide. Bull. Acad. Sci. USSR 7, 793–800 (1934) Google Scholar
- Gerrard, D.: Competition quotient: a new measure of the competition affecting individual forest trees. Research Bulletin 20, Agricultural Experiment Station, Michigan State University (1969) Google Scholar
- Grasman, R., Gramacy, R.B.: Geometry: Mesh generation and surface tesselation. R package version 0.1-7. http://CRAN.R-project.org/package=geometry (2010)
- Jain, A., Xu, X., Ho, T., Xiao, F.: Uniformity testing using minimal spanning tree. In: Proceedings of the 16th International Conference on Pattern Recognition, vol. 4, pp. 281–284 (2002) Google Scholar
- Møller, J., Waagepetersen, R.P.: Statistical Inference and Simulation for Spatial Point Processes. Chapman & Hall/CRC, London/Boca Raton (2004) Google Scholar
- Pateiro-López, B.: Set estimation under convexity-type restrictions. Ph.D. Thesis, Universidad de Santiago de Compostela (2008) Google Scholar
- Pateiro-López, B., Rodríguez-Casal, A.: Generalizing the convex hull of a sample: The R package alphahull. J. Stat. Softw. 5, 1–28 (2010) Google Scholar
- R Development Core Team.: R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna. http://www.R-project.org (2008)
- Voronoi, G.: Nouvelles applications des paramètres continus à la théorie des formes quadratiques. J. Reine Angew. Math. 133, 97–178 (1907) Google Scholar