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On the convergence of the empirical mass function

We show that the empirical mass function associated with a sequence of i.i.d. discrete random variables converges in lr at the (n/log2n)1/2 rate, for all r>=2. For r<2 the rate is shown to fail for heavy-tailed distributions. The threshold case of r=2 is explored in detail.
Year of publication:
2008
Authors: Russo, Ralph P. ; Shyamalkumar, Nariankadu D.
Published in:
Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 78.2008, 15, p. 2293-2299
Publisher: Elsevier
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Type of publication: Article
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Persistent link: https://www.econbiz.de/10005255003
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