纵向数据下自适应设计广义估计方程的大样本性质

数学物理学报 ›› 2021, Vol. 41 ›› Issue (6): 1925-1936.

纵向数据下自适应设计广义估计方程的大样本性质

尹长明*(),石岳鑫

^{广西大学数学与信息科学学院南宁 530004}

收稿日期:2020-10-26 出版日期:2021-12-26 发布日期:2021-12-02
通讯作者: 尹长明 E-mail:2814294510@qq.com
基金资助:
国家自然科学基金(11061002);国家自然科学基金(11701109);广西自然科学基金(2015GXNSFAA139006);广西自然科学基金(2018GXN-SFBA281016)

Large Sample Properties of Generalized Estimating Equations with Adaptive Designs for Longitudinal Data

Changming Yin*(),Yuexin Shi

^{School of Mathematics and Information Science, Guangxi University, Nanning 530004}

Received:2020-10-26 Online:2021-12-26 Published:2021-12-02
Contact: Changming Yin E-mail:2814294510@qq.com
Supported by:
the NSFC(11061002);the NSFC(11701109);the NSF of Guangxi(2015GXNSFAA139006);the NSF of Guangxi(2018GXN-SFBA281016)

摘要/Abstract

摘要：

广义估计方程（GEE）是分析响应变量是离散或非负的纵向数据回归问题的重要方法.该文在较弱的条件下证明了自适应设计GEE回归参数估计的渐近存在性，相合性和渐近正态性.通过数值模拟验证了估计是有效的.把Xie，Yang（Ann Statist，2003，31：310-347）和Balan，Schiopu-Kratina（Ann Statist，2005，33：522-541）的相应结果推广到了设计阵是自适应情形，并且对Fisher信息阵特征根的要求降到最低.

关键词: 广义估计方程(GEE), 自适应设计, 纵向数据, 渐近正态性

Abstract:

Generalized estimating equation (GEE) is widely adopted in analyzing longitudinal (clustered) data with discrete or nonnegative responses. In this paper, we prove the existence, weak consistency and asymptotic normality of generalized estimating equations estimator with adaptive designs under some mild regular conditions. The accuracy of the asymptotic approximation is examined via numerical simulations. Our results extend the elegant work of Xie and Yang (Ann Statist, 2003, 31: 310-347) and Balan and Schiopu-Kratina (Ann Statist, 2005, 33: 522-541).

Key words: Generalized estimating equations, Adaptive designs, Longitudinal data, Asymptotic normality

中图分类号:

O212.1

尹长明,石岳鑫. 纵向数据下自适应设计广义估计方程的大样本性质[J]. 数学物理学报, 2021, 41(6): 1925-1936.

Changming Yin,Yuexin Shi. Large Sample Properties of Generalized Estimating Equations with Adaptive Designs for Longitudinal Data[J]. Acta mathematica scientia,Series A, 2021, 41(6): 1925-1936.

图/表 2

参考文献 20

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	$\beta_{01}$ = 0.4			$\beta_{00} = -0.9$
	真实相关阵	独立相关阵	自回归相关阵	真实相关阵	独立相关阵	自回归相关阵
$n = 50$	0.3681	0.3474	0.3613	-0.9067	-0.9014	-0.9053
	(0.3861)	(0.4132)	(0.3975)	(0.2713)	(0.2741)	(0.2748)
$n = 100$	0.3990	0.3716	0.3747	-0.9057	-0.9040	-0.9055
	(0.2576)	(0.2800)	(0.2639)	(0.1830)	(0.1845)	(0.1833)
$n = 200$	0.3862	0.3837	0.3856	-0.9051	-0.9047	-0.9056
	(0.1830)	(0.1971)	(0.1868)	(0.1249)	(0.1249)	(0.1244)
$n = 400$	0.3926	0.3917	0.3920	-0.8988	-0.8987	-0.8987
	(0.1316)	(0.1411)	(0.1340)	(0.0898)	(0.0911)	(0.0903)

	$\beta_{01}$ = 0.4			$\beta_{00} = 0.9$
	真实相关阵	独立相关阵	自回归相关阵	真实相关阵	独立相关阵	自回归相关阵
$n = 50 $	0.3761	0.3480	0.3667	0.9358	0.9596	0.9437
	(0.2814)	(0.3785)	(0.3124)	(0.2873)	(0.3485)	(0.3098)
$n = 100$	0.3928	0.3778	0.3868	0.9128	0.9254	0.9178
	(0.1886)	(0.2460)	(0.2031)	(0.1955)	(0.2338)	(0.2069)
$n = 200$	0.4047	0.4018	0.4034	0.9030	0.9089	0.9045
	(0.1288)	(0.1756)	(0.1427)	(0.1371)	(0.1648)	(0.1472)
$n = 400$	0.4031	0.3961	0.4015	0.8997	0.9021	0.9006
	(0.0930)	(0.1236)	(0.1039)	(0.0938)	(0.1127)	(0.1007)

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