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A contribution to multivariate L-moments: L-comoment matrices

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  • Serfling, Robert
  • Xiao, Peng

Abstract

Multivariate statistical analysis relies heavily on moment assumptions of second order and higher. With increasing interest in heavy-tailed distributions, however, it is desirable to describe dispersion, skewness, and kurtosis under merely first order moment assumptions. Here, the univariate L-moments of Hosking [L-moments: analysis and estimation of distributions using linear combinations of order statistics, J. Roy. Statist. Soc. Ser. B 52 (1990) 105-124] are extended to "L-comoments" analogous to covariance. For certain models, the second order case yields correlational analysis coherent with classical correlation but also meaningful under just first moment assumptions. We develop properties and estimators for L-comoments, illustrate for several multivariate models, examine behavior of sample multivariate L-moments with heavy-tailed data, and discuss applications to financial risk analysis and regional frequency analysis.

Suggested Citation

  • Serfling, Robert & Xiao, Peng, 2007. "A contribution to multivariate L-moments: L-comoment matrices," Journal of Multivariate Analysis, Elsevier, vol. 98(9), pages 1765-1781, October.
    • Handle: RePEc:eee:jmvana:v:98:y:2007:i:9:p:1765-1781
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    Cited by:

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    2. Marcel Carcea & Robert Serfling, 2015. "A Gini Autocovariance Function for Time Series Modelling," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(6), pages 817-838, November.
    3. Mohan D. Pant & Todd C. Headrick, 2017. "Simulating Uniform- and Triangular- Based Double Power Method Distributions," Journal of Statistical and Econometric Methods, SCIENPRESS Ltd, vol. 6(1), pages 1-1.
    4. Asquith, William H., 2014. "Parameter estimation for the 4-parameter Asymmetric Exponential Power distribution by the method of L-moments using R," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 955-970.
    5. Qiang Zhang & Tianyao Qi & Vijay Singh & Yongqin Chen & Mingzhong Xiao, 2015. "Regional Frequency Analysis of Droughts in China: A Multivariate Perspective," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 29(6), pages 1767-1787, April.
    6. Amit Shelef & Edna Schechtman, 2019. "A Gini-based time series analysis and test for reversibility," Statistical Papers, Springer, vol. 60(3), pages 687-716, June.
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    8. Emmanuel Jurczenko & Bertrand Maillet & Paul Merlin, 2008. "Efficient Frontier for Robust Higher-order Moment Portfolio Selection," Post-Print halshs-00336475, HAL.

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