A Cramér Type Large Deviation Result for Student's t-Statistic

Qi-Man Shao
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Qi-Man Shao: University of Oregon

Journal of Theoretical Probability, 1999, vol. 12, issue 2, 385-398

Abstract: Abstract Let X, X 1, X 2,... be independent and identically distributed random variables with a finite third moment, and let T n be the Student's t-statistic. This paper shows that lim n→∞ P(T n>x)/P(t n>x)=1 holds uniformly in 0≤x≤o(n 1/6), where t n has a t-distribution with n−1 degrees of freedom. An example is also given to show that a finite third moment is necessary for this result.

Keywords: t-statistic; asymptotic distribution; self-normalized large deviation (search for similar items in EconPapers)
Date: 1999
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DOI: 10.1023/A:1021626127372

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