Abstract
In multivariate analysis, the measures of similarity and distance characterize the analogies and differences between objects. Based on the distances, a medoids test uses diversity to characterize the variabilities between and within groups. To reduce the distorting effect of outlier populations, we propose an alternative based on medians. To be precise, the medoid of each group has been related to the object that minimizes the median of the distances to the other members of the group, and the diversity within each group has been related to the median of the distances to the medoid. In this context, the distribution of the ratio of the diversities (between and within groups) is obtained by the method of permutations. The results obtained in a simulation study of a prospective character have established that, in the presence of outlier populations, the test based on medians provides a greater adherence to the level of significance (\(\alpha =0.05\)) than the test based on means.
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References
Anderson, M.J.: A new method for nonparametric multivariate analysis of variance. Austral. Ecol. 26(1), 32–46 (2001)
Hair, J.F., Black, W.C., Babin, B.J., Anderson, R.E.: Multivariate Data Analysis: A Global Perspective. Prentice Hall, Upper Saddle River (2009)
Pardo, L.: Statistical Inference Based on Divergence Measures. Chapman & Hall/CRC, Boca Raton (2006)
Salicrú, M., Morales, D., Menéndez, M.L., Pardo, L.: On the applications of divergence type measures in testing statistical hypotheses. J. Multivar. Anal. 51(2), 372–391 (1994)
Salicrú, M., Vives, S., Ocaña, J.: Testing the homogeneity of diversity measures: a general framework. J. Statist. Plan. Infer. 132(1–2), 117–129 (2005)
Seber, G.A.: Multivariate Observations. Wiley, New York (2009)
Timm, N.H.: Applied Multivariate Analysis. Springer, New York (2002)
Acknowledgements
This work was supported by the Ministerio de Ciencia, Innovación y Universidades (Spain) under Grant PID2019-104830RB-I00 and the Departament d’Empresa i Coneixement de la Generalitat de Catalunya (Spain) under Grant 2017 SGR 622 (GRBIO).
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Salicrú, M., Reverter, F., Besalú, M., Burset, M. (2023). Inference with Median Distances: An Alternative to Reduce the Influence of Outlier Populations. In: Balakrishnan, N., Gil, M.Á., Martín, N., Morales, D., Pardo, M.d.C. (eds) Trends in Mathematical, Information and Data Sciences. Studies in Systems, Decision and Control, vol 445. Springer, Cham. https://doi.org/10.1007/978-3-031-04137-2_37
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DOI: https://doi.org/10.1007/978-3-031-04137-2_37
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