TY - JOUR
T1 - On the asymptotic normality of self-normalized sums
AU - Griffin, Philip S.
AU - Mason, David M.
N1 - Funding Information:
The first author's research is supported in part by NSF Grant DMS-8700928 and the second author's research is supported in part by NSF Grant DMS-8803209.
PY - 1991
Y1 - 1991
N2 - 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.
AB - 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.
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U2 - 10.1017/S0305004100070018
DO - 10.1017/S0305004100070018
M3 - Article
AN - SCOPUS:84974306811
SN - 0305-0041
VL - 109
SP - 597
EP - 610
JO - Mathematical Proceedings of the Cambridge Philosophical Society
JF - Mathematical Proceedings of the Cambridge Philosophical Society
IS - 3
ER -