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Heavy-tailed longitudinal data modeling using copulas

Listed author(s):
  • Sun, Jiafeng
  • Frees, Edward W.
  • Rosenberg, Marjorie A.
Registered author(s):

    In this paper, we consider "heavy-tailed" data, that is, data where extreme values are likely to occur. Heavy-tailed data have been analyzed using flexible distributions such as the generalized beta of the second kind, the generalized gamma and the Burr. These distributions allow us to handle data with either positive or negative skewness, as well as heavy tails. Moreover, it has been shown that they can also accommodate cross-sectional regression models by allowing functions of explanatory variables to serve as distribution parameters. The objective of this paper is to extend this literature to accommodate longitudinal data, where one observes repeated observations of cross-sectional data. Specifically, we use copulas to model the dependencies over time, and heavy-tailed regression models to represent the marginal distributions. We also introduce model exploration techniques to help us with the initial choice of the copula and a goodness-of-fit test of elliptical copulas for model validation. In a longitudinal data context, we argue that elliptical copulas will be typically preferred to the Archimedean copulas. To illustrate our methods, Wisconsin nursing homes utilization data from 1995 to 2001 are analyzed. These data exhibit long tails and negative skewness and so help us to motivate the need for our new techniques. We find that time and the nursing home facility size as measured through the number of beds and square footage are important predictors of future utilization. Moreover, using our parametric model, we provide not only point predictions but also an entire predictive distribution.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0167-6687(07)00097-2
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    Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

    Volume (Year): 42 (2008)
    Issue (Month): 2 (April)
    Pages: 817-830

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    Handle: RePEc:eee:insuma:v:42:y:2008:i:2:p:817-830
    Contact details of provider: Web page: http://www.elsevier.com/locate/inca/505554

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    1. Cummins, J. David & Dionne, Georges & McDonald, James B. & Pritchett, B. Michael, 1990. "Applications of the GB2 family of distributions in modeling insurance loss processes," Insurance: Mathematics and Economics, Elsevier, vol. 9(4), pages 257-272, December.
    2. McDonald, James B, 1984. "Some Generalized Functions for the Size Distribution of Income," Econometrica, Econometric Society, vol. 52(3), pages 647-663, May.
    3. Manning, Willard G. & Basu, Anirban & Mullahy, John, 2005. "Generalized modeling approaches to risk adjustment of skewed outcomes data," Journal of Health Economics, Elsevier, vol. 24(3), pages 465-488, May.
    4. Lindsey, J.K. & Lindsey, P.J., 2006. "Multivariate distributions with correlation matrices for nonlinear repeated measurements," Computational Statistics & Data Analysis, Elsevier, vol. 50(3), pages 720-732, February.
    5. McDonald, James B. & Xu, Yexiao J., 1995. "A generalization of the beta distribution with applications," Journal of Econometrics, Elsevier, vol. 66(1-2), pages 133-152.
    6. Beirlant, Jan & Goegebeur, Yuri & Verlaak, Robert & Vynckier, Petra, 1998. "Burr regression and portfolio segmentation," Insurance: Mathematics and Economics, Elsevier, vol. 23(3), pages 231-250, December.
    7. Frees, Edward W. & Wang, Ping, 2006. "Copula credibility for aggregate loss models," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 360-373, April.
    8. McDonald, James B. & Butler, Richard J., 1990. "Regression models for positive random variables," Journal of Econometrics, Elsevier, vol. 43(1-2), pages 227-251.
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