Tsagris, Michail and Preston, Simon and T.A. Wood, Andrew
(2016):
*Nonparametric hypothesis testing for equality of means on the simplex.*
Forthcoming in: Journal of Statistical Computation and Simulation
No. This is a preprin of the accepted version
(2016)

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## 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.

Item Type: | MPRA Paper |
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Original Title: | Nonparametric hypothesis testing for equality of means on the simplex |

Language: | English |

Keywords: | Compositional data, hypothesis testing, Hotelling test, James test, non parametric, empirical likelihood, bootstrap |

Subjects: | C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General |

Item ID: | 72771 |

Depositing User: | Mr Michail Tsagris |

Date Deposited: | 31 Jul 2016 04:47 |

Last Modified: | 26 Sep 2019 14:38 |

References: | Aitchison, J. (1982). The statistical analysis of compositional data. Journal of the Royal Statistical Society. Series B, 44(2):139–177. Aitchison, J. (2003). The statistical analysis of compositional data. Reprinted by The Blackburn Press. Amaral, G. J. and Wood, A. T. (2010). Empirical likelihood methods for two-dimensional shape analysis. Biometrika, 97(3):757–764. Baxter, M., Beardah, C., Cool, H., and Jackson, C. (2005). Compositional data analysis of some alkaline glasses. Mathematical geology, 37(2):183–196. DiCiccio, T. and Romano, J. (1990). Nonparametric confidence limits by resampling methods and least favorable families. International Statistical Review/Revue Internationale de Statistique, 58(1):59–76. Diciccio, T. J. and Romano, J. P. (1989). On adjustments based on the signed root of the empirical likelihood ratio statistic. Biometrika, 76(3):447–456. Efron, B. (1981). Nonparametric standard errors and confidence intervals. Canadian Journal of Statistics, 9(2):139–158. 18 Egozcue, J., Pawlowsky-Glahn, V., Mateu-Figueras, G., and Barcel´o-Vidal, C. (2003). Isometric logratio transformations for compositional data analysis. Mathematical Geology, 35(3):279– 300. Emerson, S. (2009). Small sample performance and calibration of the Empirical Likelihood method. PhD thesis, Stanford university. Fisher, N. I., Hall, P., Jing, B.-Y., and Wood, A. T. (1996). Improved pivotal methods for constructing confidence regions with directional data. Journal of the American Statistical Association, 91(435):1062–1070. Fry, J., Fry, T., and McLaren, K. (2000). Compositional data analysis and zeros in micro data. Applied Economics, 32(8):953–959. Hall, P. and La Scala, B. (1990). Methodology and algorithms of empirical likelihood. International Statistical Review/Revue Internationale de Statistique, 58(2):109–127. James, G. (1954). Tests of linear hypotheses in univariate and multivariate analysis when the ratios of the population variances are unknown. Biometrika, 41(1/2):19–43. Jing, B. (1995). Two-sample empirical likelihood method. Statistics & probability letters, 24(4):315–319. Jing, B. and Robinson, J. (1997). Two-sample nonparametric tilting method. Australian Journal of Statistics, 39(1):25–34. Krishnamoorthy, K. and Yu, J. (2004). Modified nel and van der merwe test for the multivariate behrens-fisher problem. Statistics & probability letters, 66(2):161–169. Lancaster, H. (1965). The helmert matrices. American Mathematical Monthly, 72(1):4–12. Li, X., Chen, J., Wu, Y., and Tu, D. (2011). Constructing nonparametric likelihood confidence regions with high order precisions. Statistica Sinica, 21(4):1767–1783. Liu, Y., Zou, C., and Zhang, R. (2008). Empirical likelihood for the two-sample mean problem. Statistics & Probability Letters, 78(5):548–556. Mardia, K., Kent, J., and Bibby, J. (1979). Multivariate Analysis. London: Academic Press. Owen, A. (1988). Empirical likelihood ratio confidence intervals for a single functional. Biometrika, 75(2):237–249. Owen, A. (1990). Empirical likelihood ratio confidence regions. The Annals of Statistics, 18(1):90–120. Owen, A. (2001). Empirical likelihood. Boca Raton: Chapman & Hall/CRC. Preston, S. P. and Wood, A. T. (2010). Two-sample bootstrap hypothesis tests for threedimensional labelled landmark data. Scandinavian Journal of Statistics, 37(4):568–587. 19 Qin, J. and Lawless, J. (1994). Empirical likelihood and general estimating equations. The Annals of Statistics, 22(1):300–325. Rodrigues, P. C. and Lima, A. T. (2009). Analysis of an european union election using principal component analysis. Statistical Papers, 50(4):895–904. Tsagris, M. T., Preston, S., and Wood, A. T. A. (2011). A data-based power transformation for compositional data. In Proceedings of the 4rth Compositional Data Analysis Workshop, Girona, Spain. Zhou, M. (2013). emplik: Empirical likelihood ratio for censored/truncated data. R package version 0.9-9. Zhu, H., Zhou, H., Chen, J., Li, Y., Lieberman, J., and Styner, M. (2008). Adjusted exponentially tilted likelihood with applications to brain morphology. Biometrics, 65(3):919–927. 20 |

URI: | https://mpra.ub.uni-muenchen.de/id/eprint/72771 |