一类广义相依序列的概率不等式及统计推断研究

项目名称： 一类广义相依序列的概率不等式及统计推断研究

项目编号： No.11461057

项目类型： 地区科学基金项目

立项/批准年度： 2015

项目学科： 数理科学和化学

项目作者： 李永明

作者单位： 上饶师范学院

项目金额： 36万元

中文摘要： 可接受随、广义负相依和宽相依随机序列是正负相协等随机序列的一般化和推广。迄今，对这类广义相依序列概率不等式的研究较少，导致对相关统计模型的统计推断问题的研究缺乏必要的工具。为此，本项目将主要研究：1)基于这类广义相依序列， 建立Rosenthal不等式、矩不等式和Bernstein型等概率不等式；2)利用这类广义相依序列概率不等式，在完全数据和删失数据下，讨论半参数回归模型中未知参数和函数的加权核估计和小波估计的渐近性质，以及总体密度和分布函数递归核估计的大样本性质；3)利用经验似然方法等, 继续深入研究上述模型的统计推断问题；4)鉴于这类广义相依序列在风险分析中有广泛应用，为了拓广风险度量方法的适应范围和实用性，将利用非参数方法和经验似然方法，进一步研究期望损失、风险价值和条件期望损失等风险度量的估计量的渐近性质。通过本项目研究，将进一步完善相依变量的概率不等式理论及其统计推断理论。

中文关键词： 相依序列；概率不等式；小波方法；风险度量

英文摘要： Acceptable random variables and Extended negatively dependent random variables and Wide dependent random variables is a kind of random variables as generalization of Positive and Negative dependent random variables. So far, the study of probability inequality is very less for this kinds of random variables. That leads to the lack of methods and tools of studying its related statistical inference. Therefore the major issues of this project focus on the following questions: i) Based on the kind of dependent sequence, to establish several important probability inequalities as Rosenthal type inequality, moment inequalities, Bernstein type inequality, and so on. ii) By these inequalities, under full date and censored data, the asymptotic properties of the weighted kernel estimators and wavelet estimators for semiparametric regression model will be discussed for these dependent random variables mentioned above, and to establish also the large sample properties for the estimators of unknown density function and distribution function. iii) And to further study the above statistical inference problem by using empirical likelihood method. iv) In view of this kind of dependent random variables widely applied in the risk analysis, and in order to extend the range and practicability for the methods of risk measurement, by using nonparametric method and empirical likelihood method, we will further investigate the asymptotic properties of the estimators for risk measurement as Expected Shortfall, Value at Risk and Conditional Expected Shortfall. This project research can further perfect and develop the probibality inequality and statistical inference theory of dependent variable.

英文关键词： dependent sequence;probability inequality;wavelet method;risk measurement