Geodesic
On bounds for moderate deviations for Student's statistic
Teoriâ veroâtnostej i ee primeneniâ, Tome 48 (2003) no. 3, pp. 609-615

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Let $X_1,X_2,\dots$ be independent random variables with zero means and finite variances. In this paper we prove lower bounds for a Cramér-type large deviation theorem for self-normalized sums which imply that the bounds obtained by Jing, Shao, and Wang [Ann. Probab., 31 (2003), pp. 2167–2215] are sharp.
Keywords: Linnik zones, self-normalized sum, $t$-statistic, moderate deviations, nonuniform bounds. 
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     author = {G. P. Chistyakov and F. G\"otze},
     title = {On bounds for moderate deviations for {Student's} statistic},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {609--615},
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     number = {3},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TVP_2003_48_3_a11/}
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G. P. Chistyakov; F. Götze. On bounds for moderate deviations for Student's statistic. Teoriâ veroâtnostej i ee primeneniâ, Tome 48 (2003) no. 3, pp. 609-615. http://geodesic.mathdoc.fr/item/TVP_2003_48_3_a11/