Moderate deviations for two sample t-statistics
ESAIM: Probability and Statistics, Tome 11 (2007), pp. 264-271.

Let X 1 ,...,X n 1 be a random sample from a population with mean μ 1 and variance σ 1 2 , and Y 1 ,...,Y n 2 be a random sample from another population with mean μ 2 and variance σ 2 2 independent of {X i ,1in 1 }.Consider the two sample t-statistic T=X ¯-Y ¯-(μ 1 -μ 2 ) s 1 2 /n 1 +s 2 2 /n 2 . This paper shows that lnP(Tx)-x 2 /2 for any 𝑥:=𝑥(𝑛 1 ,𝑛 2 ) satisfying x, x=o(n 1 +n 2 ) 1/2 as n 1 ,n 2 provided 0<c 1 n 1 /n 2 c 2 <. If, in addition, E|X 1 | 3 <, E|Y 1 | 3 <, then P(Tx) 1-Φ(x)1 holds uniformly in x(0,o((n 1 +n 2 ) 1/6 )).

DOI : 10.1051/ps:2007020
Classification : 60F10, 60G50, 62F05
Mots clés : two sample t-statistic, asymptotic distribution, moderate deviation
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     author = {Cao, Hongyuan},
     title = {Moderate deviations for two sample $t$-statistics},
     journal = {ESAIM: Probability and Statistics},
     pages = {264--271},
     publisher = {EDP-Sciences},
     volume = {11},
     year = {2007},
     doi = {10.1051/ps:2007020},
     mrnumber = {2320820},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/ps:2007020/}
}
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Cao, Hongyuan. Moderate deviations for two sample $t$-statistics. ESAIM: Probability and Statistics, Tome 11 (2007), pp. 264-271. doi : 10.1051/ps:2007020. http://www.numdam.org/articles/10.1051/ps:2007020/

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