Strong Laws of Large Numbers for Intermediately Trimmed Sums of i.i.d. Random Variables with Infinite Mean

Marc Kesseböhmer; Tanja Schindler

doi:10.1007/s10959-017-0802-0

Strong Laws of Large Numbers for Intermediately Trimmed Sums of i.i.d. Random Variables with Infinite Mean

Marc Kesseböhmer, Tanja Schindler^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

Abstract

We show that for every sequence of nonnegative i.i.d. random variables with infinite mean there exists a proper moderate trimming such that for the trimmed sum process a non-trivial strong law of large numbers holds. We provide an explicit procedure to find a moderate trimming sequence even if the underlying distribution function has a complicated structure, e.g., has no regularly varying tail distribution.

Original language	English
Pages (from-to)	702-720
Number of pages	19
Journal	Journal of Theoretical Probability
Volume	32
Issue number	2
DOIs	https://doi.org/10.1007/s10959-017-0802-0
Publication status	Published - 1 Jun 2019

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title = "Strong Laws of Large Numbers for Intermediately Trimmed Sums of i.i.d. Random Variables with Infinite Mean",

abstract = "We show that for every sequence of nonnegative i.i.d. random variables with infinite mean there exists a proper moderate trimming such that for the trimmed sum process a non-trivial strong law of large numbers holds. We provide an explicit procedure to find a moderate trimming sequence even if the underlying distribution function has a complicated structure, e.g., has no regularly varying tail distribution.",

keywords = "Almost sure convergence theorem, Moderately trimmed sum, Strong law of large numbers",

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AU - Kesseböhmer, Marc

AU - Schindler, Tanja

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N2 - We show that for every sequence of nonnegative i.i.d. random variables with infinite mean there exists a proper moderate trimming such that for the trimmed sum process a non-trivial strong law of large numbers holds. We provide an explicit procedure to find a moderate trimming sequence even if the underlying distribution function has a complicated structure, e.g., has no regularly varying tail distribution.

AB - We show that for every sequence of nonnegative i.i.d. random variables with infinite mean there exists a proper moderate trimming such that for the trimmed sum process a non-trivial strong law of large numbers holds. We provide an explicit procedure to find a moderate trimming sequence even if the underlying distribution function has a complicated structure, e.g., has no regularly varying tail distribution.

KW - Almost sure convergence theorem

KW - Moderately trimmed sum

KW - Strong law of large numbers

UR - https://www.scopus.com/pages/publications/85038077510

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DO - 10.1007/s10959-017-0802-0

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JO - Journal of Theoretical Probability

JF - Journal of Theoretical Probability

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ER -

Strong Laws of Large Numbers for Intermediately Trimmed Sums of i.i.d. Random Variables with Infinite Mean

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