General result on precise asymptotics for self-normalized sums

Journal of East China Normal University(Natural Sc ›› 2013, Vol. 2013 ›› Issue (2): 146-153, 159.

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General result on precise asymptotics for self-normalized sums

LU Zhen-gang ¹, JIANG Yu-qiu ²

1. Propaganda Department, Siping Professional College, Siping Jilin 136002, China;
2. College of Mathematics, Jilin Normal University, Siping Jilin 136000, China

Received:2012-04-01 Revised:2012-07-01 Online:2013-03-25 Published:2013-03-20

Abstract

Abstract: Gien a sequence of i.i.d.~nondegenerate random variables
with zero means and belonging to the domain of attraction of the
normal law, by the weak convergence theorem and the tail probability
inequalities of the independent and identically distributed
sequence, a general result on precise asymptotics for the
self-normalized sums with generalized boundary functions has been
proved. It can describe the relations among the weighted function,
boundary function, convergence rate and limit value, then the known
results of this field are improved and extended.

Key words: precise asymptotics, self-normalized sums, a general result, independent and identically distributed (i.i.d.)

CLC Number:

O211.4

LU Zhen-gang, JIANG Yu-qiu. General result on precise asymptotics for self-normalized sums[J]. Journal of East China Normal University(Natural Sc, 2013, 2013(2): 146-153, 159.

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General result on precise asymptotics for self-normalized sums

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