Abstract
We establish a Berry-Esséen bound for Student's statistic for independent (nonidentically) distributed random variables. In particular, the bound implies a sharp estimate similar to the classical Berry-Esséen bound. In the i.i.d. case it yields sufficient conditions for the Central Limit Theorem for studentized sums. For non-i.i.d. random variables the bound shows that the Lindeberg condition is sufficient for the Central Limit Theorem for studentized sums.
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Research supported by the SFB 343 in Bielefeld.
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Bentkus, V., Bloznelis, M. & Götze, F. A Berry-Esséen bound for student's statistic in the non-I.I.D. case. J Theor Probab 9, 765–796 (1996). https://doi.org/10.1007/BF02214086
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DOI: https://doi.org/10.1007/BF02214086