General result on precise asymptotics for self-normalized sums

LU Zhen-gang; JIANG Yu-qiu

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Mar. 2013

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

Citation:

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

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

Citation:

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

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General result on precise asymptotics for self-normalized sums

LU Zhen-gang¹,
JIANG Yu-qiu²

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

Received Date: 2012-04-01
Rev Recd Date: 2012-07-01
Publish Date: 2013-03-25

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

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References(1)

References

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