A Two-sample Nonparametric Test for Circular Data– its Exact Distribution and Performance

S. Rao Jammalamadaka, Stéphane Guerrier () and Vasudevan Mangalam
Additional contact information
S. Rao Jammalamadaka: University of California
Stéphane Guerrier: University of Geneva
Vasudevan Mangalam: Curtin University

Sankhya B: The Indian Journal of Statistics, 2021, vol. 83, issue 1, No 8, 140-166

Abstract: Abstract A nonparametric test labelled ‘Rao Spacing-frequencies test’ is explored and developed for testing whether two circular samples come from the same population. Its exact distribution and performance relative to comparable tests such as the Wheeler-Watson test and the Dixon test in small samples, are discussed. Although this test statistic is shown to be asymptotically normal, as one would expect, this large sample distribution does not provide satisfactory approximations for small to moderate samples. Exact critical values for small samples are obtained and tables provided here, using combinatorial techniques, and asymptotic critical regions are assessed against these. For moderate sample sizes in-between i.e. when the samples are too large making combinatorial techniques computationally prohibitive but yet asymptotic regions do not provide a good approximation, we provide a simple Monte Carlo procedure that gives very accurate critical values. As is well-known, the large number of usual rank-based tests are not applicable in the context of circular data since the values of such ranks depend on the arbitrary choice of origin and the sense of rotation used (clockwise or anti-clockwise). Tests that are invariant under the group of rotations, depend on the data through the so-called ‘spacing frequencies’, the frequencies of one sample that fall in between the spacings (or gaps) made by the other. The Wheeler-Watson, Dixon, and the proposed Rao tests are of this form and are explicitly useful for circular data, but they also have the added advantage of being valid and useful for comparing any two samples on the real line. Our study and simulations establish the ‘Rao spacing-frequencies test’ as a desirable, and indeed preferable test in a wide variety of contexts for comparing two circular samples, and as a viable competitor even for data on the real line. Computational help for implementing any of these tests, is made available online “TwoCircles” R package and is part of this paper.

Keywords: Circular data; two-sample tests; spacing frequencies; small sample distributions; Wheeler-Watson; Dixon; Wilcoxon test; power.; Primary 62G10; 62E15; Secondary 62Q05 (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s13571-020-00244-9 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sankhb:v:83:y:2021:i:1:d:10.1007_s13571-020-00244-9

Ordering information: This journal article can be ordered from
http://www.springer.com/statistics/journal/13571

DOI: 10.1007/s13571-020-00244-9

Access Statistics for this article

Sankhya B: The Indian Journal of Statistics is currently edited by Dipak Dey

More articles in Sankhya B: The Indian Journal of Statistics from Springer, Indian Statistical Institute
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().