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On the limit distributions of lightly trimmed sums

Published online by Cambridge University Press:  24 October 2008

Toshio Mori
Toshio Mori
Affiliation:
Yokohama City University, Yokohama, Japan
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Extract

Let Xnn ≥ 1, be i.i.d.r.v.'s and Sn = X1+…+Xn. Let be Sn minus the r terms of largest absoluete value. Maller proved that if coverages in distribution to N(0, 1) then so does (Sn/bn)−an, assuming that Xn have a continuous symmetric distribution. We show that his resul;t is true without these extra assumptions. Some related results are also given.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 96 , Issue 3 , November 1984 , pp. 507 - 516
Copyright
Copyright © Cambridge Philosophical Society 1984

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References

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