Refined Self-normalized Large Deviations for Independent Random Variables

Qiying Wang ()
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Qiying Wang: The University of Sydney

Journal of Theoretical Probability, 2011, vol. 24, issue 2, 307-329

Abstract: 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.

Keywords: Self-normalized sum; Student t statistic; Cramér large deviation; 60F05; 60F17; 62E20 (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/s10959-011-0347-6

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