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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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
Published electronically: March 20, 2008
MathSciNet review: 2395172
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Abstract | References | Similar Articles | Additional Information

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: http://dx.doi.org/10.1090/S0002-9947-08-04402-4
PII: S 0002-9947(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