Equivalence of Regression Curves

doi:10.1080/01621459.2017.1281813

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	Equivalence of Regression Curves
	Dette, Holger 1; Moellenhoff, Kathrin 1; Volgushev, Stanislav 2,3; Bretz, Frank 4,5
刊名	JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
	2018
卷号	113 期号:522 页码:711-729
关键词	Constrained parameter estimation Equivalence of curves Keywords and phrases: Dose-response studies Nonlinear regression Parametric bootstrap
ISSN号	0162-1459
DOI	10.1080/01621459.2017.1281813
英文摘要	This article investigates the problem whether the difference between two parametric models m(1), m(2) describing the relation between a response variable and several covariates in two different groups is practically irrelevant, such that inference can be performed on the basis of the pooled sample. Statistical methodology is developed to test the hypotheses H-0: d(m(1), m(2)) >= epsilon versus H-1: d(m(1), m(2)) <= epsilon to demonstrate equivalence between the two regression curves m(1), m(2) for a prespecified threshold E, where d denotes a distance measuring the distance between m(1) and m(2). Our approach is based on the asymptotic properties of a suitable estimator d (m(1)) over cap, (m(2)) over cap of this distance. To improve the approximation of the nominal level for small sample sizes, a bootstrap test is developed, which addresses the specific form of the interval hypotheses. In particular, data have to be generated under the null hypothesis, which implicitly defines a manifold for the parameter vector. The results are illustrated by means of a simulation study and a data example. It is demonstrated that the new methods substantially improve currently available approaches with respect to power and approximation of the nominal level.
WOS研究方向	Mathematics
语种	英语
出版者	AMER STATISTICAL ASSOC
WOS记录号	WOS:000439978500020
内容类型	期刊论文
源URL	[http://10.2.47.112/handle/2XS4QKH4/784]
专题	上海财经大学
通讯作者	Dette, Holger
作者单位	1.Ruhr Univ Bochum, Fak Math, D-44780 Bochum, Germany; 2.Univ Toronto, Dept Stat Sci, Toronto, ON, Canada; 3.Univ Toronto Mississauga, Dept Math & Computat Sci, Mississauga, ON, Canada; 4.Novartis Pharma AG, Basel, Switzerland; 5.Shanghai Univ Finance & Econ, Sch Stat & Management, Shanghai, Peoples R China
推荐引用方式 GB/T 7714	Dette, Holger,Moellenhoff, Kathrin,Volgushev, Stanislav,et al. Equivalence of Regression Curves[J]. JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION,2018,113(522):711-729.
APA	Dette, Holger,Moellenhoff, Kathrin,Volgushev, Stanislav,&Bretz, Frank.(2018).Equivalence of Regression Curves.JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION,113(522),711-729.
MLA	Dette, Holger,et al."Equivalence of Regression Curves".JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION 113.522(2018):711-729.