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Central Limit Theorem by moments

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  • Blacher, René

Abstract

In a previous Central Limit Theorem by moments, it has been proved that the moments converge to those of the normal distribution if the moments of sums are asymptotically independent (cf. Blacher, R., 1990. Theoreme de la limite centrale par les moments. C. R. Acad. Sci. Paris. 311(I), 465-468). In this paper we generalize this result by adding a negligible sequence to these sums. So, we can prove that the moments of some functionals of strong mixing sequences converge.

Suggested Citation

  • Blacher, René, 2007. "Central Limit Theorem by moments," Statistics & Probability Letters, Elsevier, vol. 77(17), pages 1647-1651, November.
    • Handle: RePEc:eee:stapro:v:77:y:2007:i:17:p:1647-1651
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    References listed on IDEAS

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    1. Soulier, Philippe, 2001. "Moment bounds and central limit theorem for functions of Gaussian vectors," Statistics & Probability Letters, Elsevier, vol. 54(2), pages 193-203, September.
    2. Ibragimov, Ildar & Lifshits, Mikhail, 1998. "On the convergence of generalized moments in almost sure central limit theorem," Statistics & Probability Letters, Elsevier, vol. 40(4), pages 343-351, November.
    3. Cox, Dennis D. & Kim, Tae Yoon, 1995. "Moment bounds for mixing random variables useful in nonparametric function estimation," Stochastic Processes and their Applications, Elsevier, vol. 56(1), pages 151-158, March.
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