ON SOME TESTS FOR ELLIPTICAL SYMMETRY |
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| Affiliation: | Department of Science and Arts, China University of Mining and Technology (Beijing), Beijing 100083, China;Probability Lab, Institute of Applied Mathematics, The Chinese Academy of Sciences, Beijing 100080, China;School of Control and Computer Engineering, North China Electric Power University, Beijing 102206, China;Language & Information Sciences, University of Lausanne, 1015 Lausanne, CH, Switzerland;Key Laboratory for Applied Statistics of MOE and School of Mathematics and Statistics, Northeast Normal University, Changchun, China;Cellular Biology Section, Laboratory of Viral Diseases, National Institute of Allergy and Infectious Diseases, NIH, Bethesda, MD, United States |
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| Abstract: | In this paper, some test statistics of Kolmogorov type and Cramer-von Mises type based on projection pursuit technique are proposed for testing the sphericity problem of a high-dimensional distribution. The limiting distributions of the test statistics are derived under the null hypothesis and any fixed alternative. The asymptotic properties of Bootstrap approximation are investigated. Furthermore, for computational reasons, an approximation for the statistics, based on number theoretic method, is suggested. |
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| Keywords: | Projection pursuit type statistic test of sphericity nmumber theoretic method 62H15 62H10 |
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