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Nonparametric hypothesis testing for equality of means on the simplex

Author

Listed:
  • Tsagris, Michail
  • Preston, Simon
  • T.A. Wood, Andrew

Abstract

In the context of data that lie on the simplex, we investigate use of empirical and exponential empirical likelihood, and Hotelling and James statistics, to test the null hypothesis of equal population means based on two independent samples. We perform an extensive numerical study using data simulated from various distributions on the simplex. The results, taken together with practical considerations regarding implementation, support the use of bootstrap-calibrated James statistic.

Suggested Citation

  • Tsagris, Michail & Preston, Simon & T.A. Wood, Andrew, 2016. "Nonparametric hypothesis testing for equality of means on the simplex," MPRA Paper 72771, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:72771
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    References listed on IDEAS

    as
    1. Simon P. Preston & Andrew T. A. Wood, 2010. "Two‐Sample Bootstrap Hypothesis Tests for Three‐Dimensional Labelled Landmark Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(4), pages 568-587, December.
    2. T. Tsagris, Michail & Preston, Simon & T.A. Wood, Andrew, 2011. "A data-based power transformation for compositional data," MPRA Paper 53068, University Library of Munich, Germany.
    3. Jing, Bing-Yi, 1995. "Two-sample empirical likelihood method," Statistics & Probability Letters, Elsevier, vol. 24(4), pages 315-319, September.
    4. Jane Fry & Tim Fry & Keith McLaren, 2000. "Compositional data analysis and zeros in micro data," Applied Economics, Taylor & Francis Journals, vol. 32(8), pages 953-959.
    5. Paulo Rodrigues & Ana Lima, 2009. "Analysis of an European union election using principal component analysis," Statistical Papers, Springer, vol. 50(4), pages 895-904, August.
    6. Liu, Yukun & Zou, Changliang & Zhang, Runchu, 2008. "Empirical likelihood for the two-sample mean problem," Statistics & Probability Letters, Elsevier, vol. 78(5), pages 548-556, April.
    7. Krishnamoorthy, K. & Yu, Jianqi, 2004. "Modified Nel and Van der Merwe test for the multivariate Behrens-Fisher problem," Statistics & Probability Letters, Elsevier, vol. 66(2), pages 161-169, January.
    8. Getulio J. A. Amaral & Andrew T. A. Wood, 2010. "Empirical likelihood methods for two-dimensional shape analysis," Biometrika, Biometrika Trust, vol. 97(3), pages 757-764.
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    Cited by:

    1. Philippos Louis & Orestis Troumpounis & Nikolaos Tsakas & Dimitrios Xefteris, 2020. "Protest voting in the laboratory," "Marco Fanno" Working Papers 0247, Dipartimento di Scienze Economiche "Marco Fanno".

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    More about this item

    Keywords

    Compositional data; hypothesis testing; Hotelling test; James test; non parametric; empirical likelihood; bootstrap;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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