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Effect of kurtosis on efficiency of some multivariate medians

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  • Jin Wang
  • Weihua Zhou

Abstract

Up to now, various multivariate medians have been proposed. To support their applications, we study the effect of kurtosis on efficiency of some well-known multivariate medians. Results are established for the coordinatewise median, the spatial median, the Oja median, and their modified versions. Such results provide a basis for choosing among the multivariate medians in practical analyses. The effect of dimension on efficiency of those multivariate medians is also studied. It is found that the result of Brown [(1983), 'Statistical Uses of the Spatial Median', Journal of the Royal Statistical Society, Series B , 45, 25-30] for the spatial median and spherically symmetric normal distributions can be extended to some other medians and some non-normal distributions but does not hold in general.

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  • Jin Wang & Weihua Zhou, 2015. "Effect of kurtosis on efficiency of some multivariate medians," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 27(3), pages 331-348, September.
    • Handle: RePEc:taf:gnstxx:v:27:y:2015:i:3:p:331-348
    DOI: 10.1080/10485252.2015.1046450
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    1. Niinimaa, A. & Oja, H. & Tableman, Mara, 1990. "The finite-sample breakdown point of the Oja bivariate median and of the corresponding half-samples version," Statistics & Probability Letters, Elsevier, vol. 10(4), pages 325-328, September.
    2. Thomas P. Hettmansperger, 2002. "A practical affine equivariant multivariate median," Biometrika, Biometrika Trust, vol. 89(4), pages 851-860, December.
    3. Arevalillo, Jorge M. & Navarro, Hilario, 2012. "A study of the effect of kurtosis on discriminant analysis under elliptical populations," Journal of Multivariate Analysis, Elsevier, vol. 107(C), pages 53-63.
    4. Babu, G. Jogesh & Rao, C. Radhakrishna, 1988. "Joint asymptotic distribution of marginal quantiles and quantile functions in samples from a multivariate population," Journal of Multivariate Analysis, Elsevier, vol. 27(1), pages 15-23, October.
    5. Hannu Oja, 1999. "Affine Invariant Multivariate Sign and Rank Tests and Corresponding Estimates: a Review," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 26(3), pages 319-343, September.
    6. Oja, Hannu, 1983. "Descriptive statistics for multivariate distributions," Statistics & Probability Letters, Elsevier, vol. 1(6), pages 327-332, October.
    7. Wang, Jin, 2009. "A family of kurtosis orderings for multivariate distributions," Journal of Multivariate Analysis, Elsevier, vol. 100(3), pages 509-517, March.
    8. Srivastava, M. S., 1984. "A measure of skewness and kurtosis and a graphical method for assessing multivariate normality," Statistics & Probability Letters, Elsevier, vol. 2(5), pages 263-267, October.
    9. David E. Tyler & Frank Critchley & Lutz Dümbgen & Hannu Oja, 2009. "Invariant co‐ordinate selection," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(3), pages 549-592, June.
    10. Averous, Jean & Meste, Michel, 1994. "Multivariate kurtosis in L1-sense," Statistics & Probability Letters, Elsevier, vol. 19(4), pages 281-284, March.
    11. Wang, Jin & Zhou, Weihua, 2012. "A generalized multivariate kurtosis ordering and its applications," Journal of Multivariate Analysis, Elsevier, vol. 107(C), pages 169-180.
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    Cited by:

    1. Li, Weiming & Xu, Yangchang, 2022. "Asymptotic properties of high-dimensional spatial median in elliptical distributions with application," Journal of Multivariate Analysis, Elsevier, vol. 190(C).

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