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.
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-CI-016-04
Acknowledgements: 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).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.