基于复杂数据的回归模型统计推断及其应用

项目名称： 基于复杂数据的回归模型统计推断及其应用

项目编号： No.11501005

项目类型： 青年科学基金项目

立项/批准年度： 2016

项目学科： 数理科学和化学

项目作者： 杨文志

作者单位： 安徽大学

项目金额： 18万元

中文摘要： 在我们实际生活中存在大量的复杂数据，例如移动平均过程中的短记忆过程和长记忆过程，自回归模型数据，平稳遍历过程，各种相依数据和删失数据等等。针对这些复杂数据，本项目拟研究一些统计估计量的大样本性质，建立其强相合性、矩相合性、完全相合性、中心极限定理和Berry-Esseen 界等，并给出在回归模型等统计模型中的应用。利用极限理论和统计方法研究相依数据和删失数据的样本分位数核估计的渐近性质，建立Bahadur表示、中心极限定理和 Berry-Esseen 界等结果，并给出在风险价值VaR核估计和分位数回归模型核估计的相关应用。利用随机变量一些矩信息量，研究非负随机变量加权和的逆矩渐近逼近，以期获得更优的渐近逼近收敛速度。在此基础上用逆矩方法研究回归模型中未知参数的估计等应用问题。对上述研究的新问题及时补充跟进，通过建立新模型新方法以期获得更多理论和应用研究。

中文关键词： 非参数回归；混合样本；分位数回归；收敛速率；中心极限定理

英文摘要： There are a large number of complicated data in practice such as moving average processes including short memory process and long memory process, autoregression model data, stationary ergodic process, various dependent data and censored data. This project will investigate the properties of large sample for some statistical estimators under these complicated data. Some results such as strong consistency, mean consistency, complete consistency, uniform consistency, central limit theorem and Berry-Esseen bound, will be established, and some applications to regression models will be investigated too. With the help of limit theory and methods of statistics, asymptotic properties of kernel estimation for sample quantile are studied under dependent data and censored data, and Bahadur representation, central limit theorem and Berry-Esseen bound for sample quantile will be obtained. As applications, kernel estimations of Value-at-Risk (VaR) and quantile regression are going to be researched. By using some moment information of random variables, we study the asymptotic approximations to the inverse moments of weighted type of random variables, and try our best to get better growth rates of asymptotic approximations. Based on methods of inverse moments, we investigate some applications such as estimations of regression models. Finally, some new questions of related researches are timely studied and more results of theory and application will be obtained by building new models and new methods.

英文关键词： Nonparametric regression;Mixing sample;Quantile regression;Convergence rate;Central limit theorem