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A two-sample nonparametric test for circular data – its exact distribution and performance. (English) Zbl 1477.62108

This paper is about the development and exploration of a new test for comparing two samples on the unit circle. After studying asymptotic properties of the test statistic, the authors focus on finite sample methods for the derivation of critical values either by combinatorial techniques or Monte Carlo procedures, which on the one hand allow the practical application on real data samples and on the other hand ensure a good behavior of the test. Numerical simulations confirm this and reveal the test as a serious competitor of other state-of-the-art methods.

MSC:

62G10 Nonparametric hypothesis testing
62G20 Asymptotic properties of nonparametric inference
62R30 Statistics on manifolds
62E15 Exact distribution theory in statistics
62-08 Computational methods for problems pertaining to statistics

Software:

bootlib; TwoCircles; R
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Full Text: DOI

References:

[1] Davison, AC; Hinkley, DV, Bootstrap methods and their applications (1997), Cambridge University Press: Cambridge, Cambridge University Press · Zbl 0886.62001 · doi:10.1017/CBO9780511802843
[2] Dixon, WJ, A criterion for testing the hypothesis that two samples are from the same population, Ann. Math. Stat., 11, 199-204 (1940) · JFM 66.0644.03 · doi:10.1214/aoms/1177731914
[3] Gatto, R.; Rao, JS, A conditional saddlepoint approximation for testing problems, J. Am. Stat. Assoc., 94, 533-541 (1999) · Zbl 0997.62016 · doi:10.1080/01621459.1999.10474148
[4] Gatto, R. and Rao, J.S. (2015). On two-sample tests for circular data based on spacing-frequencies. In: Geometry Driven Statistics, Wiley Series in Probability and Statistics, (I.L. Dryden and J.T. Kent eds.) Wiley vol. 121, pp. 129-145. · Zbl 1341.62145
[5] Gibbons, JD; Chakraborti, S., Nonparametric statistical inference (2011), Boca Raton: CRC Press, Boca Raton · Zbl 1278.62004
[6] Hájek, J.; Sidak, Z.; Sen, PK, Theory of Rank Tests (1999), Cambridge: Academic Press, Cambridge · Zbl 0944.62045 · doi:10.1016/B978-012642350-1/50021-7
[7] Holst, L. and Rao, J. S. (1980). Asymptotic theory for some families of two-sample nonparametric statistics. Sankhyā: The Indian Journal of Statistics Series A, 19-52. · Zbl 0501.62032
[8] Rao, JS; SenGupta, A., Topics in Circular Statistics, 5 (2001), Singapore: World Scientific, Singapore · Zbl 1006.62050
[9] Mardia, KV; Jupp, PE, Directional Statistics, 494 (2009), Hoboken: Wiley, Hoboken
[10] Mirakhmedov, SM; Rao, JS; Mohammed, IB, On edgeworth expansions in generalized urn models, J. Theor. Probab., 27, 725-753 (2014) · Zbl 1302.62108 · doi:10.1007/s10959-012-0454-z
[11] Rao, J. S. (1976). Some tests based on arc-lengths for the circle. Sankhyā: The Indian Journal of Statistics Series B, 329-338. · Zbl 0409.62031
[12] Rao, J. S. and Murthy, V. K. (1981). A two-sample nonparametric test based on spacings frequencies. Proc. of International Statistical Institute, 43rd Session, 223-227.
[13] Schmidt-Koenig, K., Experimentelle einflußnahme auf die 24-Stunden-Periodik bei Brieftauben und deren Auswirkungen unter besonderer berücksichtigung des heimfindevermögens, Zeitschrift für Tierpsychologie, 15, 301-331 (1958) · doi:10.1111/j.1439-0310.1958.tb00568.x
[14] Taylor, A.; Burns, K., Radial distributions of air plants: A comparison between epiphytes and mistletoes, Ecology, 97, 819-825 (2016) · doi:10.1890/15-1322.1
[15] Walcott, C., Pigeon homing: observations, experiments and confusions, J. Exp. Biol., 199, 21-27 (1996) · doi:10.1242/jeb.199.1.21
[16] Wasserman, L., All of Nonparametric Statistics (2006), Berlin: Springer, Berlin · Zbl 1099.62029
[17] Wheeler, S.; Watson, G., A distribution-free two-sample test on a circle, Biometrika, 51, 256-257 (1964) · Zbl 0124.11104 · doi:10.2307/2334214
[18] Wilcoxon, F. (1945). Individual comparisons by ranking methods. Biometrics Bulletin 80-83.
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