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New Berry--Esseen-type bounds, with explicit constant factors, for the distribution of the Student statistic and, equivalently, for that of the self-normalized sum of independent zero-mean random variables are obtained.
Limit distributions of self-normalized sums
B. F. Logan, C. L. Mallows, S. O. Rice, and L. A. Shepp · 1973
Earlier work this paper cites.
Inequalities for the probability content of a rotated square and related convolutions
R. L. Hall, M. Kanter, and M. D. Perlman · 1980
Earlier work this paper cites.
A Berry-Esséen bound for Student’s statistic in the non-i.i.d. case
V. Bentkus, M. Bloznelis, and F. Götze · 1996
Earlier work this paper cites.
The Berry-Esseen bound for Student’s statistic
V. Bentkus and F. Götze · 1996
Earlier work this paper cites.
Fractional sums and integrals of r r -concave tails and applications to comparison probability inequalities
I. Pinelis · 1999
Cited alongside, same era.
On self-normalized sums
S. Y. Novak · 2000
Cited alongside, same era.
The Berry-Esseen bound for self-normalized sums
S. V. Nagaev · 2002
Cited alongside, same era.
On self-normalized sums of random variables and the Student’s statistic
S. Y. Novak · 2005
Cited alongside, same era.
Malliavin calculus and self normalized sums, preprint, arxiv:1107.0410v1 [math.PR]
S. Bourguin and C. Tudor
Cited in the paper.
Between Chebyshev and Cantelli (preprint), arXiv:1011.6065 [math.PR]
I. Pinelis
Cited in the paper.
Exact bounds on the closeness between the Student and standard normal distributions, preprint, http://arxiv.org/find/all/1/au:+pinelis/0/1/0/all/0/1
I. Pinelis
Cited in the paper.
On the Bennett-Hoeffding inequality (preprint), arXiv:0902.4058v1 [math.PR]
I. Pinelis
Cited in the paper.
Refinement of estimates of the rate of convergence in the Lyapunov theorem (preprint, in Russian)
I. Shevtsova
Cited in the paper.
I. Tyurin
Cited in the paper.
An explicit Berry-Esseen bound for Student’s t t -statistic via Stein’s method
Q.-M. Shao · 2005
Later among the works it cites.
On l’Hospital-type rules for monotonicity
I. Pinelis · 2006
Later among the works it cites.
Exact inequalities for sums of asymmetric random variables, with applications
I. Pinelis · 2007
Later among the works it cites.
Optimal two-value zero-mean disintegration of zero-mean random variables
I. Pinelis · 2009
Later among the works it cites.
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