摘要
本文考虑部分函数线性回归模型,研究了回归系数的经验似然推断,证明了所提出的经验对数似然比渐近于χ^2分布,此结果可以用来构造了相应兴趣参数的置信域.另外,本文也给出了系数函数的极大经验似然估计,并在适当条件下给出了所提出估计量的收敛速度.仅就置信域精度及其覆盖概率大小方面,通过模拟研究和实例分析比较了经验似然方法与最小二乘方法的优劣.
In this paper, we consider the partial functional linear regression model, and construct the empirical log-likelihood ratio statistic for the unknown regression parameter： It is shown that the proposed statistics have the asymptotic standard chi-square distribution, and hence they can be used to construct the confidence region of the parameter. In addition, the maximum empirical likelihood estimator of the unknown coefficient function is constructed, and its asymptotic behavior is proved. A simulation study and real data analysis are carried out to compare the proposed methods with the least-squares method in terms of the confidence regions and its coverage probabilities.
出处
《应用概率统计》
CSCD
北大核心
2015年第2期146-158,共13页
Chinese Journal of Applied Probability and Statistics
基金
国家自然科学基金(11171012
11331011)
高等学校博士学科点专项科研基金(20121103110004)
全国统计科学研究重点项目(2014LZ45)
河南省科技厅基础与前沿研究(122300413202)
北京工业大学第十三届研究生科技基金重点项目(ykj-2014-10722)
北京工业大学博士生创新基金资助
关键词
部分函数线性模型
经验似然
函数型数据
置信域
Partial functional linear regression model, empirical likelihood, functional data, confidence region.
