Towards a universal self-normalized moderate deviation

Authors:
Bing-Yi Jing, Qi-Man Shao and Wang Zhou

Journal:
Trans. Amer. Math. Soc. **360** (2008), 4263-4285

MSC (2000):
Primary 60F10, 60F15; Secondary 60G50

DOI:
https://doi.org/10.1090/S0002-9947-08-04402-4

Published electronically:
March 20, 2008

MathSciNet review:
2395172

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Abstract: This paper is an attempt to establish a universal moderate deviation for self-normalized sums of independent and identically distributed random variables without any moment condition. The exponent term in the moderate deviation is specified when the distribution is in the centered Feller class. An application to the law of the iterated logarithm is given.

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Additional Information

**Bing-Yi Jing**

Affiliation:
Department of Mathematics, Hong Kong University of Science and Technology, Hong Kong

Email:
majing@ust.hk

**Qi-Man Shao**

Affiliation:
Department of Mathematics, Hong Kong University of Science and Technology, Hong Kong – and – Department of Mathematics, University of Oregon, Eugene, Oregon 97403

Email:
maqmshao@ust.hk

**Wang Zhou**

Affiliation:
Department of Statistics and Applied Probability, National University of Singapore, Singapore 117546

Email:
stazw@nus.edu.sg

DOI:
https://doi.org/10.1090/S0002-9947-08-04402-4

Keywords:
Moderate deviation,
large deviation,
self-normalized sums,
the law of the iterated logarithm

Received by editor(s):
February 7, 2006

Received by editor(s) in revised form:
August 14, 2006

Published electronically:
March 20, 2008

Additional Notes:
The first author was supported in part by Hong Kong RGC CERG No. HKUST6117/02P and DAG05/06.SC01

The second author was partially supported by the National Science Foundation under Grant No. DMS-0103487 and HKUST DAG 05/06 Sc27 and RGC CERG No. 602206

The third author was partially supported by the grants R-155-000-035-112 and R-155-050-055-133/101 at the National University of Singapore

Article copyright:
© Copyright 2008
American Mathematical Society