Abstract
Let X 1,X 2,… , be independent random variables with EX i =0 and write \(S_{n}=\sum_{i=1}^{n}X_{i}\) and \(V_{n}^{2}=\sum_{i=1}^{n}X_{i}^{2}\). This paper provides new refined results on the Cramér-type large deviation for the so-called self-normalized sum S n /V n . The major techniques used to derive these new findings are different from those used previously.
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Wang, Q. Refined Self-normalized Large Deviations for Independent Random Variables. J Theor Probab 24, 307–329 (2011). https://doi.org/10.1007/s10959-011-0347-6
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DOI: https://doi.org/10.1007/s10959-011-0347-6