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April 2006 Inference for covariate adjusted regression via varying coefficient models
Damla Şentürk, Hans-Georg Müller
Ann. Statist. 34(2): 654-679 (April 2006). DOI: 10.1214/009053606000000083


We consider covariate adjusted regression (CAR), a regression method for situations where predictors and response are observed after being distorted by a multiplicative factor. The distorting factors are unknown functions of an observable covariate, where one specific distorting function is associated with each predictor or response. The dependence of both response and predictors on the same confounding covariate may alter the underlying regression relation between undistorted but unobserved predictors and response. We consider a class of highly flexible adjustment methods for parameter estimation in the underlying regression model, which is the model of interest. Asymptotic normality of the estimates is obtained by establishing a connection to varying coefficient models. These distribution results combined with proposed consistent estimates of the asymptotic variance are used for the construction of asymptotic confidence intervals for the regression coefficients. The proposed approach is illustrated with data on serum creatinine, and finite sample properties of the proposed procedures are investigated through a simulation study.


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Damla Şentürk. Hans-Georg Müller. "Inference for covariate adjusted regression via varying coefficient models." Ann. Statist. 34 (2) 654 - 679, April 2006.


Published: April 2006
First available in Project Euclid: 27 June 2006

zbMATH: 1095.62045
MathSciNet: MR2281880
Digital Object Identifier: 10.1214/009053606000000083

Primary: 62G08 , 62G20 , 62J05

Keywords: asymptotic normality , binning , confidence intervals , multiple regression , multiplicative effects , varying coefficient model

Rights: Copyright © 2006 Institute of Mathematical Statistics


Vol.34 • No. 2 • April 2006
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