Precise asymptotics in the deviation probability series of self-normalized sums |
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| Authors: | Dianliang Deng |
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| Affiliation: | Department of Mathematics and Statistics, University of Regina, Regina, SK, S4S 0A2 Canada |
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| Abstract: | Let X,X1,X2,… be a sequence of nondegenerate i.i.d. random variables with zero means. Set Sn=X1+?+Xn and  . In the present paper we examine the precise asymptotic behavior for the general deviation probabilities of self-normalized sums, Sn/Wn. For positive functions g(x), ?(x), α(x) and κ(x), we obtain the precise asymptotics for the following deviation probabilities of self-normalized sums: |
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| Keywords: | Precise asymptotics Complete moment convergence Deviation probability Self-normalized sums |
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