Moderate deviations for two sample t-statistics

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Abstract
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))

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