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An exponential nonuniform Berry-Esseen bound for self-normalized sums

Authors Wang, QY
Jing, Bing Yi View this author's profile
Issue Date 1999
Source Annals of probability , v. 27, (4), 1999, OCT, p. 2068-2088
Summary 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. Tn 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.
ISSN 0091-1798
Rights Published in Annals of Probability ( by the Institute of Mathematical Statistics.
Language English
Format Article
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