Tests of concentration for low-dimensional and high-dimensional directional data. (English) Zbl 1381.62088

Ahmed, S. Ejaz (ed.), Big and complex data analysis. Methodologies and applications. Cham: Springer (ISBN 978-3-319-41572-7/hbk; 978-3-319-41573-4/ebook). Contributions to Statistics, 209-227 (2017).
Summary: We consider asymptotic inference for the concentration of directional data. More precisely, we propose tests for concentration (1) in the low-dimensional case where the sample size \(n\) goes to infinity and the dimension \(p\) remains fixed, and (2) in the high-dimensional case where both \(n\) and \(p\) become arbitrarily large. To the best of our knowledge, the tests we provide are the first procedures for concentration that are valid in the \((n,p)\)-asymptotic framework. Throughout, we consider parametric FvML tests, that are guaranteed to meet asymptotically the nominal level constraint under FvML distributions only, as well as “pseudo-FvML” versions of such tests, that meet asymptotically the nominal level constraint within the whole class of rotationally symmetric distributions. We conduct a Monte-Carlo study to check our asymptotic results and to investigate the finite-sample behavior of the proposed tests.
For the entire collection see [Zbl 1392.62007].


62H11 Directional data; spatial statistics
62G20 Asymptotic properties of nonparametric inference
60E05 Probability distributions: general theory
62F03 Parametric hypothesis testing
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