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

• 成果类型: Article
• 署名作者: Wang, QY; Jing, BY
• 署名单位: University of Wollongong; Hong Kong University of Science & Technology
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1022874829
• 发表日期: 1999
• 页码: 2068-2088
• 关键词: students

摘要

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.