A BERRY-ESSEEN THEOREM FOR SAMPLE QUANTILES UNDER WEAK DEPENDENCE

• 成果类型: Article
• 署名作者: Lahiri, S. N.; Sun, S.
• 署名单位: Texas A&M University System; Texas A&M University College Station; University System of Ohio; Wright State University Dayton
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/08-AAP533
• 发表日期: 2009
• 页码: 108-126
• 关键词: asymptotic expansions; normal approximation; random vectors; sums

摘要

This paper proves a Berry-Esseen theorem for sample quantiles of strongly-mixing random variables under a polynomial mixing rate. The rate of normal approximation is shown to be O(n(-1/2)) as n -> infinity, where n denotes the sample size. This result is in sharp contrast to the case of the sample mean of strongly-mixing random variables where the rate O(n-1/2) is not known even under an exponential strong mixing rate. The main result of the paper has applications in finance and econometrics as financial time series important data often are heavy-tailed and quantile based methods play an role in various problems in finance, including hedging and risk management.