Geodesic
On self-normalized sums and Student's statistic
Teoriâ veroâtnostej i ee primeneniâ, Tome 49 (2004) no. 2, pp. 365-373

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We evaluate the accuracy of normal approximation for the distributions of some non-linear functionals of sums of random vectors. A Berry–Esseen-type inequality with explicit constants for the distribution of Student's statistic is established as a consequence of the main result.
Keywords: self-normalized sums, Student's statistic, Berry–Esseen inequality. 
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     author = {S. Yu. Novak},
     title = {On self-normalized sums and {Student's} statistic},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {365--373},
     publisher = {mathdoc},
     volume = {49},
     number = {2},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2004_49_2_a9/}
}
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S. Yu. Novak. On self-normalized sums and Student's statistic. Teoriâ veroâtnostej i ee primeneniâ, Tome 49 (2004) no. 2, pp. 365-373. http://geodesic.mathdoc.fr/item/TVP_2004_49_2_a9/