平稳相依空间数据下基于经验似然的非参数统计推断

项目名称： 平稳相依空间数据下基于经验似然的非参数统计推断

项目编号： No.11301084

项目类型： 青年科学基金项目

立项/批准年度： 2014

项目学科： 数理科学和化学

项目作者： 熊贤祝

作者单位： 福州大学

项目金额： 22万元

中文摘要： 经验似然方法是 Owen(1988,1990) 提出的一种有效的非参数统计推断方法, 它可以很好地用来构造参数的置信区间(或区域)及有效地改进统计推断。前人的研究多集中将经验似然方法应用到独立或时间序列数据，本项目将主要针对空间数据。本项目拟应用经验似然方法来构造平稳强混合相依空间数据下非参数回归函数的置信区间，并将结果延伸到平稳近邻相依空间数据上；拟研究平稳强混合相依空间数据下非参数回归函数的复加权Nadaraya-Watson估计，并将结果延伸到平稳近邻相依空间数据上；拟应用经验似然方法来分别构造平稳强混合相依空间数据下含有附加信息和不含有附加信息时条件分位数的置信区间，以及用经验似然方法来改进含有附加信息时条件分位数的核估计；拟应用经验似然方法来构造平稳强混合相依函数型空间数据下非参数回归函数的置信区间。

中文关键词： 空间数据；经验似然方法；非参数回归函数；条件分位数；点估计和区间估计

英文摘要： Empirical likelihood, introduced by Owen(1988, 1990), is an efficient method of nonparametric statistical inference, which can be well employed to construnct confidence intervals(or regions) for some parameters and to improve statistical inference efficently. Predecessors' research focuses on applying the empirical likelihood method to independent data or time series data. This project will mainly consider spatial data, the contents include the following aspects. 1) First, this project will employ the empirical likelihood method to construct confidence intervals for the nonparametric regression function under stationary and strongly mixing spatial data, and extend it to stationary and near-epoch dependent spatial data. 2) Second, this project will consider the reweighted Nadaraya-Watson estimator for the nonparametric regression function under stationary and strongly mixing spatial data, and extend it to stationary and near-epoch dependent spatial data. 3) Third, this project will employ the empirical likelihood method to construct confidence intervals for the conditional quantile in the prsence and absence of auxiliary information, respectively, under stationary and strongly mixing spatial data. In addition, this project will employ the empirical likelihood method to improve the kernel estimator of the conditi

英文关键词： spatial data；empirical likelihood；nonparametric regression function；conditional quantile；point estimate and interval estimation