Eduardo García Portugués - New uniformity tests on the hypersphere using projections
| Dates: | 19 January 2022 |
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| Times: | 14:00 - 15:00 |
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| What is it: | Seminar |
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| Organiser: | Department of Mathematics |
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| Who is it for: | University staff, External researchers, Current University students |
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| Speaker: | Eduardo García Portugués |
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Eduardo García Portugués, Associate Professor of Statistics at the Department of Statistics of Carlos III University of Madrid is our speaker for the Statistics seminar series.
Title: New uniformity tests on the hypersphere using projections
Abstract: In this talk we will introduce a projection-based class of uniformity tests on the hypersphere. The class employs statistics that integrate, along all possible directions, a weighted quadratic discrepancy between the empirical cumulative distribution of the projections and the projected uniform distribution. Simple expressions for several test statistics are obtained for the circle and the sphere, as well as relatively tractable forms for higher dimensions. Despite their different origins, variants of the proposed class are shown to contain and be contained in variants of the Sobolev class of uniformity tests. Our new class proves itself advantageous by allowing the derivation of new tests that neatly extend former circular-only tests and by introducing the ?rst instance of an Anderson–Darling-like test for directional data. Usable asymptotic distributions are discussed, while a simulation study evaluates the theoretical ?ndings. The new tests will be applied to the study of the crater distribution on Rhea. The talk is based on a joint paper with Paula Navarro-Esteban and Juan A. Cuesta-Albertos to appear in Bernoulli.
Speaker
Eduardo García Portugués
Organisation: Carlos III University of Madrid
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Zoom link: https://zoom.us/j/92947173491
