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A note on functional CLT for truncated sums

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  • Pozdnyakov, Vladimir

Abstract

Let {X,Xi}i[greater-or-equal, slanted]1 be i.i.d. random variables with a symmetric continuous distribution and EX2=[infinity], and {bn}n[greater-or-equal, slanted]1 be a sequence of increasing positive numbers. When X belongs to the Feller class, and nP(X>bn)~[gamma]n[short up arrow][infinity], a functional CLT for the truncated sums Sn=[summation operator]i=1nXiIXi[less-than-or-equals, slant]bn is proved.

Suggested Citation

  • Pozdnyakov, Vladimir, 2003. "A note on functional CLT for truncated sums," Statistics & Probability Letters, Elsevier, vol. 61(3), pages 277-286, February.
    • Handle: RePEc:eee:stapro:v:61:y:2003:i:3:p:277-286
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    References listed on IDEAS

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    1. Kasahara, Yuji, 1993. "A functional limit theorem for trimmed sums," Stochastic Processes and their Applications, Elsevier, vol. 47(2), pages 315-322, September.
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    Cited by:

    1. Pozdnyakov, Vladimir, 2004. "On the functional CLT for partial sums of truncated bounded from below random variables," Statistics & Probability Letters, Elsevier, vol. 70(2), pages 137-144, November.

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    2. Borovskikh, Yuri V. & Weber, N.C., 2008. "Asymptotic distributions of non-degenerate U-statistics on trimmed samples," Statistics & Probability Letters, Elsevier, vol. 78(4), pages 336-346, March.

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