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数学进展 - 2018, Vol. 47(2): 307-318
研究论文
AANA误差下半参数回归模型中估计量的相合性
The Consistency of Estimators in Semiparametric Regression Models under AANA Random Errors

席梦梅1,唐徐飞1,邓新1,陈维扬2,王学军1,*
XI Mengmei1, TANG Xufei1, DENG Xin1, CHEN Weiyang2, WANG Xuejun1}}

1. 安徽大学数学科学学院, 合肥, 安徽, 230601;
2. 安徽大学文典学院, 合肥, 安徽, 230601
1. School of Mathematical Sciences, Anhui University, Hefei, Anhui, 230601, P. R. China;
2. Wendian College, Anhui University, Hefei, Anhui,230601, P. R. China

出版日期: 2018-05-16
2018, Vol. 47(2): 307-318
DOI: 10.11845/sxjz.2016091b


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摘要 考虑如下半参数回归模型$$y_i=x_i\beta+g(t_i)+\sigma_ie_i, i=1,2,\cdots,n,~n\geq1,$$其中$\sigma_i^2=f(u_i),(x_i,t_i,u_i)$ 为已知设计点列. 在适当的条件下, 当误差为AANA变量时, 本文研究了未知参数$\beta$和未知函数$g$的最小二乘估计与加权最小二乘估计的相合性, 特别是$p$ ($p>1$)阶矩相合性和完全相合性, 所得结果推广了误差为NA变量的相应结论.
关键词 AANA变量半参数回归模型最小二乘估计完全相合性矩相合性    
Abstract:This paper is concerned with the semiparametric regression model $y_i=x_i\beta+g(t_i)+\sigma_ie_i$, $i=1,2,\cdots,n$, $n\geq1,$ where $\sigma_i^2=f(u_i)$, $(x_i,t_i,u_i)$ are known fixed design points. When the random errors $e_i$ are AANA random variables, some results on consistency for least squares estimators and weighted least squares estimators of $\beta$ and $g$ under some suitable conditions are investigated, especially the $p$-th ($p>1$) moment consistency and complete consistency. The results obtained in the paper generalize some corresponding ones for negatively associated random variables.
Key wordsAANA random variables    semiparametric regression model    least squares estimator    complete consistency    moment consistency
PACS:  O212.1  
基金资助:国家自然科学基金(No. 11671012); 安徽省自然科学基金(No. 1508085J06); 安徽省高校优秀拔尖人才培育资助项目(No. gxbjZD2016005)和安徽省大学生创新创业训练计划项目(Nos. 201610357313, 201610357001).
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