On the asymptotic normality of self-normalized sums

Philip S. Griffin, David M. Mason

Research output: Contribution to journalArticlepeer-review

32 Scopus citations


Let Xj, …,Xn be a sequence of non-degenerate, symmetric, independent identically distributed random variables, and let Sn(rn) denote their sum when the rn largest in modulus have been removed. We obtain necessary and sufficient conditions for asymptotic normality of the studentized version of Sn(rn), and compare this to the condition for asymptotic normality of the scalar normalized version. In particular, when rn = r these conditions are the same, but when rn → ∞ the former holds more generally.

Original languageEnglish (US)
Pages (from-to)597-610
Number of pages14
JournalMathematical Proceedings of the Cambridge Philosophical Society
Issue number3
StatePublished - 1991

ASJC Scopus subject areas

  • General Mathematics


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