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

  • Serfling, Robert
  • Xiao, Peng
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    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.

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    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 98 (2007)
    Issue (Month): 9 (October)
    Pages: 1765-1781

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    Handle: RePEc:eee:jmvana:v:98:y:2007:i:9:p:1765-1781
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    1. Schechtman, E. & Yitzhaki, S., 1999. "On the proper bounds of the Gini correlation," Economics Letters, Elsevier, vol. 63(2), pages 133-138, May.
    2. Elamir, Elsayed A. H. & Seheult, Allan H., 2003. "Trimmed L-moments," Computational Statistics & Data Analysis, Elsevier, vol. 43(3), pages 299-314, July.
    3. Rubinstein, Mark E., 1973. "The Fundamental Theorem of Parameter-Preference Security Valuation," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 8(01), pages 61-69, January.
    4. Lerman, Robert I. & Yitzhaki, Shlomo, 1984. "A note on the calculation and interpretation of the Gini index," Economics Letters, Elsevier, vol. 15(3-4), pages 363-368.
    5. Robert F. Dittmar, 2002. "Nonlinear Pricing Kernels, Kurtosis Preference, and Evidence from the Cross Section of Equity Returns," Journal of Finance, American Finance Association, vol. 57(1), pages 369-403, 02.
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