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    Efficient Semiparametric Marginal Estimation for the Partially Linear Additive Model for Longitudinal/Clustered Data

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    Type
    Article
    Authors
    Carroll, Raymond
    Maity, Arnab
    Mammen, Enno
    Yu, Kyusang
    KAUST Grant Number
    KUS-CI-016-04
    Date
    2009-04-23
    Online Publication Date
    2009-04-23
    Print Publication Date
    2009-05
    Permanent link to this record
    http://hdl.handle.net/10754/598118
    
    Metadata
    Show full item record
    Abstract
    We consider the efficient estimation of a regression parameter in a partially linear additive nonparametric regression model from repeated measures data when the covariates are multivariate. To date, while there is some literature in the scalar covariate case, the problem has not been addressed in the multivariate additive model case. Ours represents a first contribution in this direction. As part of this work, we first describe the behavior of nonparametric estimators for additive models with repeated measures when the underlying model is not additive. These results are critical when one considers variants of the basic additive model. We apply them to the partially linear additive repeated-measures model, deriving an explicit consistent estimator of the parametric component; if the errors are in addition Gaussian, the estimator is semiparametric efficient. We also apply our basic methods to a unique testing problem that arises in genetic epidemiology; in combination with a projection argument we develop an efficient and easily computed testing scheme. Simulations and an empirical example from nutritional epidemiology illustrate our methods.
    Citation
    Carroll R, Maity A, Mammen E, Yu K (2009) Efficient Semiparametric Marginal Estimation for the Partially Linear Additive Model for Longitudinal/Clustered Data. Stat Biosci 1: 10–31. Available: http://dx.doi.org/10.1007/s12561-009-9000-7.
    Sponsors
    Yu and Mammen’s research was supported by the Deutsche Forschungsgemein-schaft project MA 1026/7-3. Carroll and Maity’s research was supported by a grant from the NationalCancer Institute (CA57030). Carroll’s work was also supported by Award Number KUS-CI-016-04, madeby King Abdullah University of Science and Technology (KAUST).
    Publisher
    Springer Nature
    Journal
    Statistics in Biosciences
    DOI
    10.1007/s12561-009-9000-7
    PubMed ID
    20161464
    PubMed Central ID
    PMC2791377
    ae974a485f413a2113503eed53cd6c53
    10.1007/s12561-009-9000-7
    Scopus Count
    Collections
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