2009
DOI: 10.1093/biomet/asp015
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Nonparametric additive regression for repeatedly measured data

Abstract: We develop an easily computed smooth backfitting algorithm for additive model fitting in repeated measures problems. Our methodology easily copes with various settings, such as when some covariates are the same over repeated response measurements. We allow for a working covariance matrix for the regression errors, showing that our method is most efficient when the correct covariance matrix is used. The component functions achieve the known asymptotic variance lower bound for the scalar argument case. Smooth ba… Show more

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Cited by 25 publications
(24 citation statements)
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“…In this section, we describe the local linear smooth backfitting estimator for repeated measures data (Carroll et al 2009), state its properties when an additive model holds, and then describe its properties when the additive model fails. The latter result is new.…”
Section: Local Linear Smooth Backfitting and Its Propertiesmentioning
confidence: 99%
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“…In this section, we describe the local linear smooth backfitting estimator for repeated measures data (Carroll et al 2009), state its properties when an additive model holds, and then describe its properties when the additive model fails. The latter result is new.…”
Section: Local Linear Smooth Backfitting and Its Propertiesmentioning
confidence: 99%
“…The minimizer of (3) exists and is given as follows (Carroll et al 2009). Define the following estimators, for q = 1, … , D , r = 0,1,2, utrue^sr(x)=j=1Jbjj,Σn1i=1ntrue(Xitaliciqjxhqtrue)rKhq(x,Xitaliciqj) and for q , p = 1, … , D ; r , s = 0,1, trueυ^qitalicrs(x,y)=j=1Jk=1,jJbjk,Σn1i=1ntrue(Xitaliciqjxhqtrue)rtrue(Xitaliciqkyhqtrue)sKhq(x,Xitaliciqj)Khq(y,Xiqk);trueυ^italicqpitalicrs(x,y)=j=1Jk=1Jbjk,Σn1i=1ntrue(…”
Section: Local Linear Smooth Backfitting and Its Propertiesmentioning
confidence: 99%
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“…Here we pursue a different kind of additivity that occurs in the time domain rather than in the spectral domain and develop nonlinear functional regression models that are not dependent on a preliminary functional principal component analysis yet are structurally stable and not weighed down by the curse of dimensionality (Hall et al 2009). Additive models (Friedman & Stuetzle 1981;Stone 1985) have been successfully used for many regression situations that involve continuous predictors and both continuous and generalized responses (Mammen & Park 2005;Yu et al 2008;Carroll et al 2008). …”
Section: Introductionmentioning
confidence: 99%
“…Carroll et al (2009) had the same observation for a special case with repeated measurement data when g is the identity function.…”
Section: Estimation Methodsmentioning
confidence: 62%