Towards a universal self-normalized moderate deviation

Jing, Bing-Yi; Shao, Qi-Man; Zhou, Wang

doi:10.1090/S0002-9947-08-04402-4

Towards a universal self-normalized moderate deviation
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by Bing-Yi Jing, Qi-Man Shao and Wang Zhou PDF

Trans. Amer. Math. Soc. 360 (2008), 4263-4285 Request permission

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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