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On the heavy-tailedness of Student's t-statistic
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Mathematical Statistics.
2011 (English)In: Bernoulli, ISSN 1350-7265, Vol. 17, no 1, 276-289 p.Article in journal (Refereed) Published
Abstract [en]

Let {X-i}(i >= 1) be an i.i.d. sequence of random variables and define, for n >= 2, T-n={(n-1/2 (sigma) over capn-1Sn)(0), ((sigma) over capn > 0,)((sigma) over capn=0,) with S-n = Sigma(n)(i=1) X-i, (sigma) over cap (2)(n)=1/n-1 Sigma(n)(i=1)(X-i - n(-1)S(n))(2). We investigate the connection between the distribution of an observation X-i and finiteness of E vertical bar T-n vertical bar(r) for (n, r) is an element of N->= 2 x R+. Moreover, assuming T-n ->(d) T, we prove that for any r > 0, lim(n ->infinity) E vertical bar T-n vertical bar(r) = E vertical bar T vertical bar(r) < infinity, provided there is an integer n(0) such that E vertical bar T-n0 vertical bar(r) is finite.

Place, publisher, year, edition, pages
2011. Vol. 17, no 1, 276-289 p.
Keyword [en]
finiteness of moments, robustness, Student's t-statistic, t-distributions, t-test
National Category
URN: urn:nbn:se:uu:diva-149782DOI: 10.3150/10-BEJ262ISI: 000288042800013OAI: oai:DiVA.org:uu-149782DiVA: diva2:405660
Available from: 2011-03-23 Created: 2011-03-23 Last updated: 2011-04-05Bibliographically approved

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Jonsson, Fredrik
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Mathematical Statistics
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