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The central limit problem for trimmed sums

Published online by Cambridge University Press:  24 October 2008

Philip S. Griffin  and
William E. Pruitt
Philip S. Griffin
Affiliation:
Department of Mathematics, Syracuse University, Syracuse, NY 13210, U.S.A.
William E. Pruitt
Affiliation:
School of Mathematics, University of Minnesota, Minneapolis, MN 55455, U.S.A.
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Extract

Let X, X1, X2,… be a sequence of non-degenerate i.i.d. random variables with common distribution function F. For 1 ≤ j ≤ n, let mn(j) be the number of Xi satisfying either |Xi| > |Xj|, 1 ≤ i ≤ n, or |Xi| = |Xj|, 1 ≤ i ≤ j, and let (r)Xn = Xj if mn(j) = r. Thus (r)Xn is the rth largest random variable in absolute value from amongst X1, …, Xn with ties being broken according to the order in which the random variables occur. Set (r)Sn = (r+1)Xn + … + (n)Xn and write Sn for (0)Sn. We will refer to (r)Sn as a trimmed sum.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 102 , Issue 2 , September 1987 , pp. 329 - 349
Copyright
Copyright © Cambridge Philosophical Society 1987

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References

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