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

作　　者：席梦梅 唐徐飞 邓新[1] 陈维扬 王学军[1] XI Mengmei1, TANG Xufei1, DENG Xin1, CHEN Weiyang2, WANG Xuejun1(1. School of Mathematical Sciences, Anhui University, Hefei, Anhui, 230601, P. R. China 2. Wendian College, Anhui University, Hefei, Anhui, 230601, P. R. Chin)

机构地区：[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

出　　处：《数学进展》2018年第2期307-318,共12页Advances in Mathematics（China）

基　　金：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);安徽省大学生创新创业训练计划项目(Nos.201610357313;201610357001)

摘　　要：考虑如下半参数回归模型y_i=x_iβ+g(t_i)+σ_ie_i,i=1,2,…,n,n≥1,其中σ_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β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.This paper is concerned with the semiparametric regression modelyi=xiβ＋g（ti）＋σiei,i=1,2,…,n,n≥1 are whereσi^2=f（ui）,（xi,ti,ui） are known fixed design points. When the random errors ei are AANA random variables, some results on consistency for least squares estimators and weighted least squares estimators of β and g under some suitable condi- tions 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.

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 

分 类 号：O212.1[理学—概率论与数理统计]