Issue |
ESAIM: PS
Volume 11, February 2007
Special Issue: "Stochastic analysis and mathematical finance" in honor of Nicole El Karoui's 60th birthday
|
|
---|---|---|
Page(s) | 264 - 271 | |
DOI | https://doi.org/10.1051/ps:2007020 | |
Published online | 19 June 2007 |
Moderate deviations for two sample t-statistics
Department of Statistics and Operations Research, University of North
Carolina-Chapel Hill, Chapel Hill, NC 27599, USA; hycao@email.unc.edu
Received:
14
July
2006
Revised:
12
December
2006
Let X1,...,Xn1 be a
random sample from a population with mean µ1 and variance
, and X1,...,Xn1 be a random sample from
another population with mean µ2 and variance
independent of
{Xi,1 ≤ i ≤ n1}.
Consider the two
sample t-statistic
.
This paper shows that
ln P(T ≥ x) ~ -x²/2 for any x := x(n1,n2)
satisfying x → ∞, x = o(n1 + n2)1/2 as n1,n2 → ∞ provided 0 < c1 ≤ n1/n2 ≤ c2 < ∞. If, in
addition, E|X1|3 < ∞, E|Y1|3 < ∞, then
holds uniformly in x ∈ (O,o((n1 + n2)1/6))
Mathematics Subject Classification: 60F10 / 60G50 / 62F05
Key words: Two sample t-statistic / asymptotic distribution / moderate deviation.
© EDP Sciences, SMAI, 2007
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