A note on functional CLT for truncated sums

Let {X,Xi}i[greater-or-equal, slanted]1 be i.i.d. random variables with a symmetric continuous distribution and EX2=[infinity], and {bn}n[greater-or-equal, slanted]1 be a sequence of increasing positive numbers. When X belongs to the Feller class, and nP(X>bn)~[gamma]n[short up arrow][infinity], a functional CLT for the truncated sums Sn=[summation operator]i=1nXiIXi[less-than-or-equals, slant]bn is proved.

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Year of publication:	2003
Authors:	Pozdnyakov, Vladimir
Published in:	Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 61.2003, 3, p. 277-286
Publisher:	Elsevier
Keywords:	Functional CLT Truncated sums Trimmed sums Martingale

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

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