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Towards a universal self-normalized moderate deviation |
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| Authors: | Bing-Yi Jing Qi-Man Shao Wang Zhou |
| Institution: | Department of Mathematics, Hong Kong University of Science and Technology, Hong Kong ; Department of Mathematics, Hong Kong University of Science and Technology, Hong Kong -- and -- Department of Mathematics, University of Oregon, Eugene, Oregon 97403 ; Department of Statistics and Applied Probability, National University of Singapore, Singapore 117546 |
| 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. |
| Keywords: | Moderate deviation large deviation self-normalized sums the law of the iterated logarithm |
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