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October 1999 An Exponential Nonuniform Berry-Esseen Bound for Self-Normalized Sums
Bing-Yi Jing, Qiying Wang
Ann. Probab. 27(4): 2068-2088 (October 1999). DOI: 10.1214/aop/1022874829


In this paper we shall derive exponential nonuniformBerry–Esseen bounds in the central limit theorem for self-normalized sums.We show that the size of the error can be reduced considerably by replacing the usual standardization by self-normalization. In particular, we establish the exponential bounds for the probability of the self-normalized sums under the condition that the third moment is finite, whereas an exponential moment assumption is required for the standardized sums. Applications to t-statistics and the probabilities of moderate deviations of self-normalized sums are also discussed.


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Bing-Yi Jing. Qiying Wang. "An Exponential Nonuniform Berry-Esseen Bound for Self-Normalized Sums." Ann. Probab. 27 (4) 2068 - 2088, October 1999.


Published: October 1999
First available in Project Euclid: 31 May 2002

zbMATH: 0972.60011
MathSciNet: MR1742902
Digital Object Identifier: 10.1214/aop/1022874829

Primary: 60F10 , 60F15
Secondary: 60G50 , 62F03

Keywords: Berry–Esseen bound , Moderate deviation , nonuniformestimate , self-normalized sum , t-statistics

Rights: Copyright © 1999 Institute of Mathematical Statistics


Vol.27 • No. 4 • October 1999
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