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Asymptotic normality of lightly trimmed means – a converse

Published online by Cambridge University Press:  24 October 2008

R. A. Maller
R. A. Maller
Affiliation:
CSIRO, Division of Mathematics and Statistics, Wembley, Western Australia
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Extract

Let Xi be iidrv's and Sn = X1 + X2 + … + Xn. Let (r)Sn be Sn minus the r terms of largest absolute value. If (Sn/Bn)− An converges to normality for some Bn, An, then so does ((r)Sn/Bn) − An. We show that the converse is true if Xi have a continuous symmetric distribution, and give some related results.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 92 , Issue 3 , November 1982 , pp. 535 - 545
Copyright
Copyright © Cambridge Philosophical Society 1982

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References

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