# zbMATH — the first resource for mathematics

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].

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