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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2018, Vol. 35 ›› Issue (4): 385-407.doi: 10.3969/j.issn.1005-3085.2018.04.003

• • 上一篇    下一篇

强混合样本情形含附加信息时总体分位数的经验似然置信区间

黎   玲1,   李华英2,   罗   敏3,   秦永松2   

  1. 1- 梧州职业学院机电工程系，梧州  543002
    2- 广西师范大学数学与统计学院，桂林  541004
    3- 桂林市职工大学数学系，桂林  541002
  • 收稿日期:2016-10-28 接受日期:2017-09-06 出版日期:2018-08-15 发布日期:2018-10-15
  • 基金资助:
    国家自然科学基金(11671102)；广西自然科学基金(2016GXNSFAA3800163)；广西高校数学与统计模型重点实验室基金.

Empirical Likelihood Confidence Intervals for Quantiles in the Presence of Auxiliary Information under Strong Mixing Samples

LI Ling1,   LI Hua-ying2,   LUO Min3,   QIN Yong-song2   

  1. 1- Department of Mechanical and Electrical Engineering, Wuzhou Vocational College, Wuzhou 543002
    2- College of Mathematics and Statistics, Guangxi Normal University, Guilin 541004
    3- Department of Mathematics, Guilin Staff and Workers University, Guilin 541002
  • Received:2016-10-28 Accepted:2017-09-06 Online:2018-08-15 Published:2018-10-15
  • Supported by:
    The National Natural Science Foundation of China (11671102); the Natural Science Foundation of Guangxi (2016GXNSFAA3800163); the Foundation of Key Laboratory of Mathematics and Statistics in Universities of Guangxi.

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摘要： 强混合随机变量序列的应用较为广泛，如许多线性过程为强混合的，且一些连续时间扩散模型和随机波动模型为强混合的．在金融风险管理领域分位数又称VaR，它表示给定置信水平下金融资产产生的损失的上限．本文在强混合样本和含附加信息情形构造了总体分位数的对数经验似然比统计量，并证明了对数经验似然比统计量的渐近分布为卡方分布，由此构造了总体分位数的经验似然置信区间．在此基础上考虑了一类检验问题，证明了在同一检验水平下，含附加信息时检验的渐近功效高于不含附加信息时检验的渐近功效，并且含附加信息时检验的渐近功效随信息量的增加而非降．

关键词: 强混合样本, 附加信息, 分位数, 分组经验似然, 渐近功效

Abstract: Strong mixing random variable sequences are used widely in practice. For example, linear processes are strongly mixing under certain conditions. In addition, some continuous time diffusion models and stochastic volatility models are strongly mixing as well. In financial risk management, population quantiles are also called VaR (Value-at-Risk) which specifies the level of excessive losses at a given confidence level. In this paper, in the presence of auxiliary information and under  strong mixing samples, the log-empirical likelihood ratio statistics for quantiles are proposed and it is shown that these statistics asymptotically have the distribution of $\chi^2$. Based on this result, the empirical likelihood based confidence intervals for quantiles are constructed. A class of testing problems are also investigated. It is shown that the asymptotic power of the testing rule in the presence of auxiliary information is higher than that without auxiliary information, and the power is not decreased as more information is available.

Key words: strong mixing sample, auxiliary information, quantile, blockwise empirical likelihood, asymptotic power

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