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Asymptotic expansions of densities of sums of random vectors without third moment

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  • Peng, Liang
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    Abstract

    Asymptotic expansions of densities of the normalized sums of random vectors with at least finite third moment have been studied extensively (Normal Approximation and Asymptotic expansions. Wiley, New York.). In this note, we obtain the asymptotic expansions of densities of the normalized sums of i.i.d. random vectors with regularly varying density with index between 4 and 5, which implies that third moment is infinite.

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 58 (2002)
    Issue (Month): 2 (June)
    Pages: 167-174

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    Handle: RePEc:eee:stapro:v:58:y:2002:i:2:p:167-174

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    Keywords: Asymptotic expansion Characteristic function Potter bounds Regular variation;

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    1. de Haan, L. & Omey, E. & Resnick, S., 1984. "Domains of attraction and regular variation in IRd," Journal of Multivariate Analysis, Elsevier, vol. 14(1), pages 17-33, February.
    2. Nagaev, Alexander V. & Zaigraev, Alexander Yu., 1998. "Multidimensional Limit Theorems Allowing Large Deviations for Densities of Regular Variation," Journal of Multivariate Analysis, Elsevier, vol. 67(2), pages 385-397, November.
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