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Title: An exponential nonuniform Berry-Esseen bound for self-normalized sums
Authors: Wang, Qiying
Jing, Bing-Yi
Keywords: Berry-Esseen bound
Self-normalized sum
Moderate deviation
Nonuniform estimate
Issue Date: Oct-1999
Citation: The annals of probability, 1999, v. 27, no. 4, p. 2068-2088
Abstract: In this paper we shall derive exponential nonuniform Berry-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.
Rights: Published in Annals of Probability ( by the Institute of Mathematical Statistics.
Appears in Collections:MATH Journal/Magazine Articles

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