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A functional limit theorem for trimmed sums

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  • Kasahara, Yuji

Abstract

This paper proves a functional limit theorem for Stigler's result on the heavily trimmed sums of i.i.d. random variables. The limiting process will be expressed as a functional of a Kiefer process and we shall also see that it is a Brownian motion if and only if asymptotic normality holds.

Suggested Citation

  • Kasahara, Yuji, 1993. "A functional limit theorem for trimmed sums," Stochastic Processes and their Applications, Elsevier, vol. 47(2), pages 315-322, September.
    • Handle: RePEc:eee:spapps:v:47:y:1993:i:2:p:315-322
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    Cited by:

    1. Pozdnyakov, Vladimir, 2003. "A note on functional CLT for truncated sums," Statistics & Probability Letters, Elsevier, vol. 61(3), pages 277-286, February.
    2. 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.
    3. 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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