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Convergence in distribution of lightly trimmed and untrimmed sums are equivalent

Published online by Cambridge University Press:  24 October 2008

Harry Kesten
Harry Kesten
Affiliation:
Department of Mathematics, White Hall, Cornell University, Ithaca NY 14853, U.S.A.
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Abstract

We show that trimming a fixed number of terms from sums of i.i.d. random variables (so-called light trimming) can have only a modest effect on limiting behaviour. More specifically, the trimmed sums, after centralization and normalization, have a limit distribution, if and only if the untrimmed sums have a limit distribution (with the same centralization and normalization constants).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 113 , Issue 3 , May 1993 , pp. 615 - 638
Copyright
Copyright © Cambridge Philosophical Society 1993

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