Please wait a minute...
北京大学期刊网 | 作者  审稿人  编委专家  工作人员

首页   |   关于   |   浏览   |   投稿指南   |   新闻公告
数学进展 - 2018, Vol. 47(2): 307-318
The Consistency of Estimators in Semiparametric Regression Models under AANA Random Errors

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

[369 KB]

    /   /   推荐

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).
[1] Chandra, T.K. and Ghosal, S., Extensions of the strong law of large numbers of Marcinkiewicz and Zygmund for dependent variables, Acta Math. Hungar., 1996, 71(4): 327-336.
[2] Chen, M.H., Ren, Z. and Hu, S.H., Strong consistency of a class of estimators in partial linear model, Acta Math. Sin., Chin. Ser., 1998, 41(2): 429-438 (in Chinese).
[3] Chen, Z.Y., Liu, T.T., Chen, Z.Q. and Wang, X.J., Strong law of large numbers and strong convergence rate for AANA sequence, J. Hefei Univ. Technol. Nat. Sci., 2012: 35(12): 1725-1728 (in Chinese).
[4] Chen, Z.Y., Wang, X.J. and Hu, S.H., Strong laws of large numbers for weighted sums of asymptotically almost negatively associated random variables, Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Math. RACSAM}, 2015, 109(1): 135-152.
[5] Engle, R.F., Granger, C.W.J., Rice, J. and Weiss, A., Semiparametric estimates of the relation between weather and electricity sales, J. Amer. Statist. Assoc., 1986, 81(394): 310-320.
[6] Gao, J.T., Consistency of estimation in a semiparametric regression model (I), J. Systems Sci. Math. Sci., 1992, 12(3): 269-272 (in Chinese).
[7] Gao, J.T., Convergence rates of some estimators for a semiparametric regression model, J. Univ. Sci. Technol. China, 1992, 22(2): 129-137.
[8] Gao, J.T., Chen, X.R. and Zhao, L.C., Asymptotic normality of a class of estimators in partial linear models, Acta Math. Sin., Chin. Ser., 1994, 37(2): 256-268 (in Chinese).
[9] Hu, H.C. and Zhang, Y., Strong consistency of $M$-estimation in linear regression model with AANA errors, Adv. Math. (China), 2016, 45(3): 463-470 (in Chinese).
[10] Joag-Dev, K. and Proschan, F., Negative association of random variables, with applications, Ann. Statist., 1983, 11(1): 286-295.
[11] Ko, M.H., Kim, T.S. and Lin, Z.Y., The Hájeck-Rènyi inequality for the AANA random variables and its applications, Taiwanese J. Math., 2005, 9(1): 111-122.
[12] Ren, Z. and Chen, M.H., Strong consistency of a class of estimators in partial linear model for negative associated samples, Chinese J. Appl. Probab. Statist., 2002, 18(1): 60-66 (in Chinese)
[13] Shen, A.T., Zhang, Y. and Volodin, A., Applications of the Rosenthal-type inequality for negatively superadditive dependent random variables, Metrika, 2015, 78(3): 295-311.
[14] Wang, X.H., Shen, A.T. and Li, X.Q., A note on complete convergence of weighted sums for array of rowwise AANA random variables, J. Inequal. Appl., 2013, 2013: Article ID 359, 13 pp.
[15] 吴群英, 混合序列的概率极限理论, 北京: 科学出版社, 2006.
[16] Yuan, D.M. and An, J., Rosenthal type inequalities for asymptotically almost negatively associated random variables and applications, Sci. China Math., 2009, 52(9): 1887-1904.
[17] Zhang, Y., Hu, H.C. and Zeng, Z., Central limit theorems for AANA random sequence, Pure Appl. Math. (Xi'an), 2016, 32(1): 36-44 (in Chinese).
[18] Zhou, X.C. and Hu, S.H., Moment consistency of estimators in semi-parametric regression model under NA samples, Pure Appl. Math. (Xi'an), 2010, 26(2): 262-269 (in Chinese).
[1] 王春雨, 田茂再. 分层混合效应模型迭代广义最小二乘估计的大样本性质[J]. 数学进展, 2018, 47(4): 613-623.
[2] 胡宏昌. 误差为MA\mbox{\boldmath $(\infty)$}序列的半参数回归模型小波估计的渐近正态性[J]. 数学进展, 2013, 42(4): 551-562.
[3] 胡宏昌;胡迪鹤;. 鞅差时间序列半参数回归模型的小波估计[J]. 数学进展, 2010, 39(1): 23-30.
Full text



首页 · 关于 · 关于OA · 法律公告 · 收录须知 · 联系我们 · 注册 · 登录

© 2015-2017 北京大学图书馆 .