纵向数据下自适应设计广义估计方程的大样本性质

Abstract

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

CLC Number:

O212.1

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.

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

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